Calculates QTL effects in multi-environment trials or multiple populations (M.P Boer, M. Malosetti, S.J. Welham & J.T.N.M. Thissen).
Options
PRINT = string tokens |
What to print (summary, model, components, effects, means, stratumvariances, monitoring, vcovariance, deviance, Waldtests, missingvalues, covariancemodels); default summ |
|---|---|
POPULATIONTYPE = string token |
Type of population (BC1, DH1, F2, RIL, BCxSy, CP); must be set |
NGENERATIONS = scalar |
Number of generations of selfing for a RIL population |
NBACKCROSSES = scalar |
Number of backcrosses for a BCxSy population |
NSELFINGS = scalar |
Number of selfings for a BCxSy population |
VCMODEL = string token |
Specifies the variance-covariance model for the set of environments or populations (identity, diagonal, cs, hcs, outside, fa, fa2, unstructured); default cs for multi-environment trials, and diagonal for multiple populations |
VCPARAMETERS = string token |
Whether to re-estimate the variance-covariance model parameters (estimate, fix); default esti |
VCSELECT = string token |
Whether to re-select the variance-covariance model (no, yes); default no |
CRITERION = string token |
Criterion to use for model selection (aic, sic); default sic |
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 for a multi-environment trial |
POPULATIONS = factors |
Population factor; must be set for a multiple-population analysis |
UNITERROR = variates |
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 |
SELECTEDMODEL = texts |
VCMODEL setting for the selected covariance structure |
ADDITIVEPREDICTORS = pointers |
Additive genetic predictors; must be set |
ADD2PREDICTORS = pointers |
Second (paternal) set of additive genetic predictors |
DOMINANCEPREDICTORS = pointers |
Dominance genetic predictors |
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; must be set |
MKLOCI = variates |
Logical variate containing the value 1 if the locus is a marker, otherwise 0; must be set |
IDMGENOTYPES = texts |
Labels for the genotypes corresponding to the genetic predictors |
IDPARENTS = texts |
Labels to identify the parents |
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 or QTL-by-population interaction |
DOMSELECTED = variates |
Logical variate indicating whether the dominance predictor of each selected QTL must be present (1) or absent (0) in the model |
DOMINTERACTIONS = variates |
Logical variate indicating whether the dominance-by-environment or dominance-by-population interaction of each selected QTL must be present (1) or absent (0) in the model |
RESIDUALS = variates |
Residuals from the analysis |
FITTEDVALUES = variates |
Fitted values from the analysis |
WALDSTATISTICS = variates |
Saves the Wald test statistics |
PRWALD = variates |
Saves the associated Wald probabilities |
DFWALD = variates |
Saves the degrees of freedom for the Wald test |
QEFFECTS = pointers |
Saves the estimated QTL effects |
QSE = pointers |
Saves the standard errors of the QTL effects |
OUTFILENAME = texts |
Name of the Genstat workbook file (*.gwb) to be created |
QSAVE = pointers |
Saves a pointer with information and results for the significant effects |
SAVE = REML save structures |
Save the details of each REML analysis for use in subsequent VDISPLAY and VKEEP directives |
Description
QMESTIMATES fits a final QTL model to estimate QTL effects in a multi-environment trial or for multiple populations. The procedure uses means per genotype-environment or genotype-population combinations as phenotypic data, but weights can be attached to the means (see the UNITERROR parameter and the UNITFACTOR option below). 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. The POPULATIONTYPE option must be set to specify the population from which the genotypes are derived. For recombinant inbred lines (POPULATIONTYPE = RIL), the NGENERATIONS option, must be set to supply the number of generations. For backcross inbred lines (POPULATIONTYPE = BCxSy), the NBACKCROSSES and NSELFINGS options must be set to define the number of backcrosses to the first parent and the number of selfings, respectively. For a multiple-population analysis, the POPULATIONS parameter should be set (to a factor) instead of ENVIRONMENTS.
Molecular information must be provided in the form of additive genetic predictors stored in variates and supplied, in a pointer, by the ADDITIVEPREDICTORS parameter. Non-additive effects can be included in the model by specifying dominance genetic predictors using the DOMINANCEPREDICTORS parameter (e.g. in a F2 population). In the case of segregating F1 populations (outbreeders) two sets of additive genetic predictors must be specified, the maternal ones by the ADDITIVEPREDICTORS parameter, and the paternal ones by the ADD2PREDICTORS parameter. The corresponding map information for the genetic predictors must be given by the CHROMOSOMES and POSITIONS parameters. The labels for the loci must be supplied by the IDLOCI parameter, and the labels for the genotypes in the marker data can be supplied by the IDMGENOTYPES parameter. If IDMGENOTYPES is set, the match between the genotypes in the phenotypic and in the marker data will be checked. The IDPARENTS parameter can supply labels to identify the parents.
The QTL model assumes ENVIRONMENTS (or POPULATIONS) and QTLs as fixed terms, and GENOTYPES as a random term. The QTLSELECTED parameter must specify the set of QTLs, 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 (or populations), and one if it is specific for each environment (or population). When the DOMINANCEPREDICTORS parameter is set, the DOMSELECTED parameter supplies a logical variate containing one if the dominance predictor of the corresponding marker must be present in the model, and zero if the dominance predictor of the corresponding marker must be absent in the model. If DOMINANCEPREDICTORS is set but DOMSELECTED is not set, all the dominance predictors are included. Similarly, the DOMINTERACTIONS parameter supplies a logical variate containing one if the dominance-by-environment (or dominance-by-population) interaction of the corresponding marker must be present in the model, and zero if it must be absent. If DOMINANCEPREDICTORS is set but DOMINTERACTIONS is not set, all the dominance predictors are included.
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 (or populations). The VCMODEL option defines the model to use for Σ. The default assumes compound symmetry, but the VGESELECT procedure can be used to assess what model would be most suitable. Initial values for the parameters in the variance-covariance model can be specified by the VCINITIAL parameter. The VCPARAMETERS option controls whether the variance-covariance parameters are re-estimated at each step of the backward selection (VCPARAMETERS=estimate), or whether they are fixed at the defined initial values (VCPARAMETERS=fix). The VCSELECT option defines whether an extra check is made at each step on the variance-covariance model, to assess whether a simpler model is more suitable than the current model (based on the criterion defined by the CRITERION option). The SELECTEDMODEL parameter stores the final variance-covariance model that is selected.
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 QTLs retained in the model, and the other settings correspond to those in the PRINT option of the REML directive.
The QTL effects and their standard errors can be saved, in pointers, by the QEFFECTS and QSE parameters, respectively. These pointers have 2 levels of suffixes: the first level has 1, 2 or 3 values depending on the setting of the 3 possible predictors ADDITIVEPREDICTORS, ADD2PREDICTORS and DOMINANCEPREDICTORS; the second level has as many levels as the number of levels of the ENVIRONMENTS (or POPULATIONS) factor. The fitted values and residuals can be saved by the FITTEDVALUES and RESIDUALS parameters. The Wald statistics, degrees of freedom and probabilities can be saved by the parameters WALDSTATISTICS, DFWALD and PRWALD, respectively.
The OUTFILENAME parameter can be used to save the Wald statistics and the QEFFECTS and QSE structures in a Genstat work book file in a sheet named STATISTICS. This parameter should not contain an extension as the extension is defined automatically as .gwb.
The QSAVE parameter can be used to save a pointer containing information and results for the significant QTLs. The elements of the pointer are labelled as follows to simplify their subsequent use:
'procedure' |
stores the string 'QMESTIMATE' to indicate the source of the results, |
|---|---|
'trait' |
trait, |
'markernames' |
marker names, |
'chromosomes' |
chromosomes, |
'positions' |
positions, |
'envnames' |
names of the environments (or populations), |
'waldstatistics' |
wald statistics, |
'prwald' |
probability values of wald statistics, |
'dfwald' |
degrees of freedom of the wald statistics, |
'qeffects' |
QTL effects, |
'qse' |
standard errors of the QTL effects, |
'%vexplained' |
percentage variance explained, |
'lowerci' |
lower bound of confidence interval of estimated QTL position, |
'upperci' |
upper bound of confidence interval of estimated QTL position, |
'posmin' |
position of left flanking marker, |
'posmax' |
position of right flanking marker, |
'idlfm' |
marker name of left flanking marker, |
'idrfm' |
marker name of right flanking marker, |
'posminci' |
position of left flanking marker outside confidence interval, |
'posmaxci' |
position of right flanking marker outside confidence interval, |
'idlfmci' |
marker name of left flanking marker outside confidence interval, |
'idrfmci' |
marker name of right flanking marker outside confidence interval, |
'locus' |
index numbers of the significant QTLs, and |
'neff' |
number of additive and dominance predictors in the model. |
The elements 'procedure', 'trait', 'markernames', 'chromosomes', 'envnames', 'idlfm', 'idrfm', 'idlfmci' and 'idrfmci' are text structures; 'positions', 'waldstatistics', 'prwald' and 'dfwald' are variates; 'qeffects' and 'qse' are pointers (see parameters QEFFECTS and QSE), as similarly are 'lowerci', 'upperci', 'posmin', 'posmax', 'posminci', 'posmaxci', 'idlfmci' and 'idrfmci'; 'neff' is a scalar.
The SAVE parameter can be used to save the REML save structure from the analysis for use with subsequent VKEEP and VDISPLAY directives.
Options: PRINT, POPULATIONTYPE, NGENERATIONS, NBACKCROSSES, NSELFINGS, VCMODEL, VCPARAMETERS, VCSELECT, CRITERION, FIXED, UNITFACTOR,MVINCLUDE, MAXCYCLE, WORKSPACE.
Parameters: TRAIT, GENOTYPES, ENVIRONMENTS, POPULATIONS, UNITERROR, VCINITIAL, SELECTEDMODEL, ADDITIVEPREDICTORS, ADD2PREDICTORS, DOMINANCEPREDICTORS, CHROMOSOMES, POSITIONS, IDLOCI, IDMGENOTYPES, IDPARENTS, QTLSELECTED, INTERACTIONS, DOMSELECTED, DOMINTERACTIONS, RESIDUALS, FITTEDVALUES, WALDSTATISTICS, PRWALD, DFWALD, QEFFECTS, QSE, OUTFILENAME, QSAVE, SAVE.
Method
QMESTIMATE fits the following models, which include a set L of QTLs:
1) yij = μ + Ej + Σl∈L xiladd αjladd + GEij
if only ADDITIVEPREDICTORS are specified
2) yij = μ + Ej + Σl∈L ( xiladd αjladd + xildom αjldom ) + GEij
if DOMINANCEPREDICTORS are also specified
3) yij = μ + Ej + Σl∈L ( xiladd αjladd + xiladd2 αjladd2 + xildom αjmldom ) + GEij
if both ADD2PREDICTORS and DOMINANCEPREDICTORS are specified (for population type CP)
where yij is the trait value of genotype i in environment (or population) j, Ej is the environment (or population) main effect, xiladd are the additive genetic predictors of genotype i for locus l, and αjladd are the associated effects. In models 2 and 3, xildom are the dominance genetic predictors, and αjldom are the associated effects. In model 3, xiladd are the additive genetic predictors for maternal genotype i at locus l, xiladd2 are the additive genetic predictors for paternal genotype i, and αjladd and αjladd2 are the associated effects. Genetic predictors are genotypic covariables that reflect the genotypic composition of a genotype at a specific chromosome location (Lynch & Walsh 1998). GEij is assumed to follow a multi-Normal distribution with mean vector 0, and a variance covariance matrix Σ, that can either be modelled explicitly (with an unstructured model) or by some parsimonious model (defined by option VCMODEL) as described in the VGESELECT procedure.
Action with RESTRICT
Restrictions are not allowed.
Reference
Lynch, M. & Walsh, B. (1998). Genetics and Analysis of Quantitative Traits. Sinauer Associates, Sunderland, MA.
See also
Procedures: QMBACKSELECT, QMQTLSCAN, QMVAF, QFLAPJACK, QREPORT, VGESELECT.
Commands for: Statistical genetics and QTL estimation.
Example
CAPTION 'QMESTIMATE example'; STYLE=meta
SPLOAD [PRINT=*] '%GENDIR%/Examples/F2maize_traits.gsh'
& '%GENDIR%/Examples/F2maizemarkers.GWB'; SHEET='LOCI'
& '%GENDIR%/Examples/F2maizemarkers.GWB'; SHEET='ADDPREDICTORS'
& '%GENDIR%/Examples/F2maizemarkers.GWB'; SHEET='DOMPREDICTORS'
POINTER [MODIFY=yes; NVAL=idlocus] addpred
POINTER [MODIFY=yes; NVAL=idlocus] dompred
" Best variance-covariance model from VGESELECT "
TEXT model; VALUE= 'fa'
" Candidate QTL positions from QMBACKSELECT "
VARIATE [VALUES=19,41,237] Qid
VARIATE [VALUES=1,1,1] Int
VARIATE [VALUES=1,1,1] Dom
VARIATE [VALUES=1,0,0] DomInt
QMESTIMATE [PRINT=summ,model,wald,eff; POPULATIONTYPE=F2; VCMODEL=#model]\
TRAIT=yld; ENVIRONMENTS=E; GENOTYPES=G;\
CHROMOSOMES=mkchr; POSITIONS=mkpos; MKLOCI=marker;\
IDLOCI=idlocus; ADDITIVEPREDICTORS=addpred;\
DOMINANCEPREDICTORS=dompred;\
QTLSELECTED=Qid; INTERACTIONS=Int;\
DOMSELECTED=Dom; DOMINTERACTIONS=DomInt;\
QEFF=Qeff; QSE=Qse; QSAVE=Output;\
OUTFILE='F2maize_qmestimate'