Forms the components of a diallel model for `REML`

or regression (R.W. Payne).

### No options

### Parameters

`MALEPARENTS` = factors |
Specifies the male parents |
---|---|

`FEMALEPARENTS` = factors |
Specifies the female parents |

`PARENTS` = matrices |
Saves design matrices for the overall parental effects |

`COMPPARENTS` = matrices |
Saves comparison matrices for overall parental effects |

`PUREVSCROSS` = factors |
Saves factors to represent the comparison between pure and crossed lines |

`CROSSPAIR` = factors |
Saves factors to represent the comparison between types of pairs of parent (ignoring the individual genders) |

### Description

`FDIALLEL`

forms the factors and matrices that are needed to specify and fit a diallel model using Genstat `REML`

or regression.

The factors identifying the male and female parent of each line are specified by the `MALEPARENTS`

and `FEMALEPARENTS`

parameters, respectively. The `PARENTS`

parameter saves a design matrix that can be used in `REML`

to represent the overall effects of each parental line, and the `COMPPARENTS`

parameter saves the transpose of the matrix. You can use `COMPPARENTS`

as the third argument of the `COMPARISON`

function to fit the parental effects in a Genstat regression model. The `PUREVSCROSS`

parameter saves a factor to represent the comparison between pure and crossed lines, and the `CROSSPAIR`

parameter saves a factor representing the comparison between types of pairs of parent (ignoring their individual genders).

The examples for `FDIALLEL`

(which can be accessed by using the `LIBEXAMPLE`

procedure or the Examples menu in Genstat *for Windows*) show how these factors and matrices can be used in Genstat `REML`

and regression to generate the analyses of Hayman (1954) and Jones (1965), provided by the `DIALLEL`

procedure. The terms in the `DIALLEL`

analysis correspond to those in the `FDIALLEL`

analysis as follows.

a: variation between mean effects of each parental line; this corresponds to `PARENTS`

in `REML`

, or `COMP(Vdum;`

`np;`

`COMPPARENTS)`

in regression (where `vdum`

is a dummy variate, containing any values, and `np`

is the number of different types of parental line).

b1: assesses whether dominance is largely uni-directional; corresponds to `PUREVSCROSS`

.

b2: estimates “asymmetry” i.e. if alleles at any one locus are not equally frequent; corresponds to `PARENTS.PUREVSCROSS`

in `REML`

, or `COMP(Vdum;`

`np;`

`COMPPARENTS).PUREVSCROSS`

in regression.

b3: signifies that some dominance is peculiar to individual crosses; corresponds to `CROSSPAIR`

.

c: variation between average maternal effects of each parental line; corresponds to `FEMALEPARENT`

.

d: variation in the reciprocal differences not attributable to c; corresponds to `MALEPARENT.FEMALEPARENT`

.

Options: none.

Parameters: `MALEPARENTS`

, `FEMALEPARENTS`

, `PARENTS`

, `COMPPARENTS`

, `PUREVSCROSS`

, `CROSSPAIR`

.

### Action with `RESTRICT`

`FDIALLEL`

ignores restrictions i.e. it forms the factors and matrices using all the units of `MALEPARENTS`

and `FEMALEPARENTS`

.

### References

Hayman, B.I. (1954). The Analysis of Variance of Diallel Tables. *Biometrics*, 10, 235-244.

Jones, R.M. (1965). Analysis of Variance of the Half Diallel Table. *Heredity*, 20, 117-121.

### See also

Procedures: `DIALLEL`

, `FCONTRASTS`

.

Commands for: Regression analysis, REML analysis of linear mixed models.

### Example

CAPTION 'FDIALLEL examples',\ !t('Data from Hayman, B.I. (1954). Biometrics 10, 235-244.',\ 'Two blocks of 8 x 8 full diallel tables.'); STYLE=meta,plain TEXT [VALUES=one,two,three,four,five,six,seven,eight] Parents FACTOR [NVALUES=128; LABELS=Parents] Male,Female FACTOR [NVALUES=128; LEVELS=2] Blocks READ Blocks,Female,Male,Y; FREPRESENTATION=levels,2(labels),* 1 one one 276 1 one two 156 1 one three 322 1 one four 250 1 one five 162 1 one six 193 1 one seven 222 1 one eight 152 1 two one 136 1 two two 166 1 two three 164 1 two four 134 1 two five 102 1 two six 150 1 two seven 96 1 two eight 90 1 three one 246 1 three two 158 1 three three 416 1 three four 213 1 three five 160 1 three six 222 1 three seven 128 1 three eight 166 1 four one 318 1 four two 132 1 four three 218 1 four four 272 1 four five 138 1 four six 195 1 four seven 108 1 four eight 124 1 five one 150 1 five two 124 1 five three 164 1 five four 164 1 five five 156 1 five six 158 1 five seven 100 1 five eight 114 1 six one 182 1 six two 136 1 six three 204 1 six four 216 1 six five 133 1 six six 174 1 six seven 112 1 six eight 120 1 seven one 174 1 seven two 86 1 seven three 194 1 seven four 142 1 seven five 86 1 seven six 92 1 seven seven 58 1 seven eight 94 1 eight one 152 1 eight two 128 1 eight three 158 1 eight four 136 1 eight five 126 1 eight six 114 1 eight seven 84 1 eight eight 142 2 one one 302 2 one two 178 2 one three 274 2 one four 246 2 one five 140 2 one six 204 2 one seven 254 2 one eight 154 2 two one 142 2 two two 175 2 two three 136 2 two four 128 2 two five 128 2 two six 174 2 two seven 116 2 two eight 114 2 three one 242 2 three two 174 2 three three 360 2 three four 178 2 three five 140 2 three six 208 2 three seven 160 2 three eight 154 2 four one 204 2 four two 138 2 four three 206 2 four four 210 2 four five 130 2 four six 192 2 four seven 138 2 four eight 176 2 five one 180 2 five two 140 2 five three 156 2 five four 146 2 five five 176 2 five six 192 2 five seven 104 2 five eight 170 2 six one 186 2 six two 146 2 six three 202 2 six four 222 2 six five 150 2 six six 166 2 six seven 136 2 six eight 176 2 seven one 162 2 seven two 100 2 seven three 162 2 seven four 100 2 seven five 98 2 seven six 84 2 seven seven 48 2 seven eight 142 2 eight one 154 2 eight two 138 2 eight three 140 2 eight four 144 2 eight five 124 2 eight six 112 2 eight seven 96 2 eight eight 166 : CAPTION 'Hayman analysis'; STYLE=meta " form factors and matrices for analysis " FDIALLEL MALEPARENTS=Male; FEMALEPARENTS=Female; PARENTS=Parent;\ COMPPARENTS=Parentm; PUREVSCROSS=Pure_vs_Cross; CROSSPAIR=b3 VARIATE [VALUES=128(0)] Parentv MODEL Y FIT [PRINT=accumulated; NOMESSAGE=aliasing] \ Blocks + (Pure_vs_Cross * COMP(Parentv;8;Parentm)) \ + b3 + Female + Male.Female \ + Blocks.(Pure_vs_Cross * COMP(Parentv;8;Parentm)) \ + Blocks.(b3 + Female) VCOMPONENTS [FIXED=Blocks + (Pure_vs_Cross * Parent) \ + b3 + Female + Male.Female \ + Blocks.(Pure_vs_Cross * Parent) \ + Blocks.(b3 + Female)] REML Y CAPTION 'Griffing analysis'; STYLE=meta " form factors and matrices for analysis " FDIALLEL MALEPARENTS=Male; FEMALEPARENTS=Female; PARENTS=GCA;\ COMPPARENTS=GCAm; CROSSPAIR=SCA VARIATE [VALUES=128(0)] GCAv MODEL Y FIT [PRINT=accumulated; NOMESSAGE=aliasing] \ Blocks + COMP(GCAv;8;GCAm) + SCA + Female + Male.Female VCOMPONENTS [FIXED=Blocks + GCA + SCA + Female + Male.Female] REML Y CAPTION 'Compare with DIALLEL '; STYLE=meta " put data into two matrices (one for each block) as required by DIALLEL " MATRIX [ROWS=8; COLUMNS=8] Blockdat[1...2] EQUATE Y; NEWSTRUCTURE=Blockdat DIALLEL [PRINT=aov,griffing; LABELS=Parents] Blockdat[] CAPTION !t('Data from Jones, R.M. (1965). Heredity 20, 117-121.',\ 'Single block of half diallel.') FACTOR [NVALUES=10; LEVELS=4] male,female READ male,female,y 1 1 33.9 1 2 42.0 1 3 35.6 1 4 38.7 2 2 31.0 2 3 36.7 2 4 39.1 3 3 30.0 3 4 34.5 4 4 32.8 : CAPTION 'Hayman analysis'; STYLE=meta " form factors and matrices for analysis " FDIALLEL MALEPARENTS=male; FEMALEPARENTS=female; PARENTS=parent;\ COMPPARENTS=parentm; PUREVSCROSS=pure_vs_cross; CROSSPAIR=b3 CALCULATE parentv = y - y MODEL y FIT [PRINT=accumulated; NOMESSAGE=aliasing] \ (COMP(parentv;3;parentm) * pure_vs_cross) + b3 " regression analysis shows that b3 has to be used as the residual " VCOMPONENTS [FIXED=parent * pure_vs_cross] REML y CAPTION 'Compare with DIALLEL '; STYLE=meta " read data in a matrix (as required for DIALLEL) " MATRIX [ROWS=4; COLUMNS=4] Data READ Data 33.9 42.0 35.6 38.7 0 31.0 36.7 39.1 0 0 30.0 34.5 0 0 0 32.8 : DIALLEL [PRINT=aov; METHOD=half] Data