Calculates percentage variance accounted for by QTL effects in a multi-environment analysis (S.J. Welham, M.P. Boer, M.Malosetti & J.T.N.M. Thissen).

### Options

`PRINT` = string token |
What to print (`summary` ); default `summ` |
---|---|

`SELECTION` = string tokens |
What types of statistics to calculate (`add` , `drop` , `cumulative` ); default `add` , `drop` , `cumu` |

`METHOD` = string tokens |
What methods to use to calculate the percentage variance accounted for (`trace` , `determinant` ); default `trac` , `dete` |

`VCMODEL` = string token |
Specifies the variance-covariance model for the set of environments (`identity` , `diagonal` , `cs` , `hcs` , `outside` , `fa` , `fa2` , `unstructured` ); default `cs` |

`FIXED` = formula |
Defines extra fixed effects |

`UNITFACTOR` = factor |
Saves the units factor required to define the random model when `UNITERROR` is to be used |

`MVINCLUDE` = string tokens |
Whether to include units with missing values in the explanatory factors and variates and/or the y-variates (`explanatory` , `yvariate` ); default `expl` , `yvar` |

`MAXCYCLE` = scalar |
Limit on the number of iterations; default 100 |

`WORKSPACE` = scalar |
Number of blocks of internal memory to be set up for use by the `REML` algorithm; default 100 |

### Parameters

`TRAIT` = variates |
Quantitative trait to be analysed; must be set |
---|---|

`GENOTYPES` = factors |
Genotype factor; must be set |

`ENVIRONMENTS` = factors |
Environment factor; must be set |

`UNITERROR` = variate |
Uncertainty on trait means (derived from individual unit or plot error) to be included in QTL analysis; default `*` i.e. omitted |

`VCINITIAL` = pointers |
Initial values for the parameters of the variance-covariance model |

`ADDITIVEPREDICTORS` = pointers |
Additive genetic predictors; must be set |

`CHROMOSOMES` = factors |
Chromosomes corresponding to the genetic predictors; must be set |

`POSITIONS` = variates |
Positions on the chromosomes corresponding to the genetic predictors; must be set |

`IDLOCI` = texts |
Labels for the loci |

`QTLSELECTED` = variates |
Index numbers of the selected QTLs; must be set |

`INTERACTIONS` = variates |
Logical variate indicating whether each selected QTL has a significant (1) or non-significant (0) QTL-by-environment interaction |

`OUTFILENAME` = texts |
Name of the Genstat workbook file (`*.gwb` ) to be created |

### Description

`QMVAF`

calculates the percentage variance accounted for by estimated QTL effects in a multi-environment trial. The response variable must be specified by the `TRAIT`

parameter, and the corresponding environment and genotype factors must be specified by the `ENVIRONMENTS`

and `GENOTYPES`

parameters, respectively. Molecular information used in the original analysis must be provided in the form of additive genetic predictors stored in variates and supplied, in a pointer, by the `ADDITIVEPREDICTORS`

parameter. The corresponding map information for the genetic predictors must be given by the `CHROMOSOMES`

and `POSITIONS`

parameters. The labels for the loci can be supplied by the `IDLOCI`

parameter.

The QTL model assumes `ENVIRONMENTS`

and QTLs as fixed terms, and `ENVIRONMENTS.GENOTYPES`

as random term. The `QTLSELECTED`

parameter must specify the set of QTLs in the final model, in the form of a variate containing the index number of the positions where the QTLs are located. The `INTERACTIONS`

parameter supplies a logical variate containing zero if a QTL effect is constrained to be constant across environments, and one if it is specific for each environment (QTL × environment interaction present). Extra fixed effects can be defined by the `FIXED`

option. A multi-Normal distribution, with vector mean 0 and variance covariance matrix Σ is assumed for the random genetic effects in the different environments. The `VCMODEL`

option defines the model to use for Σ, which should be the same as that used to identify the set of QTL effects. Initial values for the parameters in the variance-covariance model can be specified by the `VCINITIAL`

parameter and the parameters will be re-estimated for each internal fit of the model.

The `MVINCLUDE`

, `MAXCYCLE`

and `WORKSPACE`

options operate in the same way as these options of the `REML`

directive. The `UNITERROR`

parameter allows uncertainty on the trait means (derived from individual unit or plot error) to be specified to include in the random model; by default this is omitted. The `UNITFACTOR`

option allows the factor that is needed to define the unit-error term to be saved (this would be needed, for example, to save information later about the term using `VKEEP`

).

The `PRINT`

option specifies the output to be displayed. The `summary`

setting prints the information about the percentage variance accounted for by QTLs in the model.

The `METHOD`

option specifies the method to use to calculate the percentage variance accounted for. This can be done by calculating the change in either the trace or determinant of the fitted covariance model. The trace and determinant correspond to the arithmentic and geometric means of the eigenvalues of the covariance matrix, respectively.

The `SELECTION`

option specifies the statistics to be calculated, with the following settings:

`add` |
the impact of adding a single QTL term is calculated by comparing the total variance (measured by trace or determinant) under the baseline model (which contains only the `ENVIRONMENTS` factor and any extra fixed terms specified using the `FIXED` option) with the total variance under a model containing a single QTL term, partitioned into main effect and (if present) interaction in addition to main effect; each of the QTL terms specified by the `QTLSELECTED` parameter is tested in turn; |
---|---|

`drop` |
the comparison is between the full model (containing the `ENVIRONMENTS` factor, any extra `FIXED` terms, and all QTL terms specified by the `QTLSELECTED` parameter) and models excluding each one of the QTL terms, in turn; again this is partitioned into main effect and (if present) interaction; and |

`cumulative` |
a model is built up by adding in first all main effects and then all interaction terms, calculating the percentage variance accounted for at each step; the order in which the terms are added is determined by the percentage variance accounted for by individual terms. |

The `OUTFILENAME`

parameter can be used to save the summary statistics in a Genstat workbook. This workbook has one page for each type of statistic (determined by the settings of `SELECTION`

option) calculated using each method (determined by the settings of option `METHOD`

). This parameter should not contain an extension as the extension is defined automatically as `.gwb`

.

Options: `PRINT`

, `SELECTION`

, `METHOD`

, `VCMODEL`

, `FIXED`

, `UNITFACTOR,MVINCLUDE`

, `MAXCYCLE`

, `WORKSPACE`

.

Parameters: `TRAIT`

, `GENOTYPES`

, `ENVIRONMENTS`

, `UNITERROR`

, `VCINITIAL`

, `ADDITIVEPREDICTORS`

, `CHROMOSOMES`

, `POSITIONS`

, `IDLOCI`

, `QTLSELECTED`

, `INTERACTIONS`

, `OUTFILENAME`

.

### Method

`QMVAF`

works with the models fitted by `QMESTIMATE`

, which include a set *L* of QTLs:

*y _{ij}* =

*μ*+

*E*+ Σ

_{j}_{l∈L}

*x*

_{il}*α*+

_{jl}*GE*

_{ij}where *y _{ij}* is the trait value of genotype

*i*in environment

*j*,

*E*is the environment main effect,

_{j}*x*are the additive genetic predictors of genotype

_{il}*i*for locus

*l*, and

*α*are the associated effects. A variance matrix Σ (defined by option

_{jl}`VCMODEL`

) is fitted within line across environments, with independence across lines. Additional fixed terms may be specified by using option `FIXED`

.`QMVAF`

compares the fit of two models, that differ according to QTL effects that they contain, by looking at the change in the trace or the determinant of the across-environment variance matrix Σ. The trace considers the average change in within-environment variances, whilst the determinant also considers the impact on across-environment covariances. The variance matrix obtained by fitting the model without any QTL terms gives a measure of total variance, which is used as the denominator in all comparisons.

### Action with `RESTRICT`

Restrictions are not allowed.

### See also

Procedures: `QMBACKSELECT`

, `QMESTIMATE`

, `QMQTLSCAN`

, `VGESELECT`

.

Commands for: Statistical genetics and QTL estimation.

### Example

CAPTION 'QMVAF example'; STYLE=meta SPLOAD [PRINT=*] '%GENDIR%/Examples/F2maize_traits.gsh' & '%GENDIR%/Examples/F2maizemarkers.gwb'; SHEET='LOCI' & '%GENDIR%/Examples/F2maizemarkers.gwb'; SHEET='ADDPREDICTORS' " Best variance-covariance model from VGESELECT " TEXT model; VALUE= 'fa' " Candidate QTL positions from QMBACKSELECT " VARIATE [VALUES=9,41,63,88,133] Qid VARIATE [VALUES=2(1),0,2(1)] Int QMESTIMATE [PRINT=summary,model,wald; POPULATIONTYPE=F2;\ VCMODEL=#model] TRAIT=yld; ENVIRONMENTS=E; GENOTYPES=G;\ CHROMOSOMES=mkchr; POSITIONS=mkpos; MKLOCI=marker;\ IDLOCI=idlocus; ADDITIVEPREDICTORS=addpred; QTLSELECTED=Qid;\ INTERACTIONS=Int; QEFF=Qeff; QSE=Qse QMVAF [VCMODEL=#model] TRAIT=yld; ENVIRONMENTS=E; GENOTYPES=G;\ CHROMOSOMES=mkchr; POSITIONS=mkpos; ADDITIVEPREDICTORS=addpred;\ QTLSELECTED=Qid; INTERACTIONS=Int