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QMVAF procedure

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).


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


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


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.




QMVAF works with the models fitted by QMESTIMATE, which include a set L of QTLs:

yij = μ + Ej + ΣlL xil αjl + GEij

where yij is the trait value of genotype i in environment j, Ej is the environment main effect, xil are the additive genetic predictors of genotype i for locus l, and αjl are the associated effects. A variance matrix Σ (defined by option 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


Commands for: Statistical genetics and QTL estimation.


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
              CHROMOSOMES=mkchr; POSITIONS=mkpos; ADDITIVEPREDICTORS=addpred;\ 
Updated on March 6, 2019

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