Performs a QTL backward selection for loci 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 |
ALPHALEVEL = scalar |
Defines a significance level; default 0.05 |
VCMODEL = string token |
Defines the variance-covariance model for the set of environments (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 |
IDMGENOTYPES = texts |
Labels for the genotypes corresponding to the genetic predictors |
QTLCANDIDATES = variates |
Specifies the locus index numbers from which to start the selection; must be set |
QTLSELECTED = variates |
Saves the index numbers of the selected QTLs |
INTERACTIONS = variates |
Saves a logical variate indicating whether each selected QTL showed a significant (1) or non-significant (0) QTL-by-environment or QTL-by-population interaction |
DOMSELECTED = variates |
Saves a logical variate indicating whether each selected QTL showed a significant (1) or non-significant (0) effect of the DOMINANCEPREDICTORS |
DOMINTERACTIONS = variates |
Saves a logical variate indicating whether each selected QTL showed a significant (1) or non-significant (0) dominance-by-environment or dominance-by-population interaction |
WALDSTATISTICS = variates |
Saves the Wald test statistics |
PRWALD = variates |
Saves the associated Wald probabilities |
Description
QMBACKSELECT selects QTLs by backward selection from a list of candidate QTLs (loci) in multi-environment trials. Alternatively, it can analyse data from multiple populations. It 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 have been derived. 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 can 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 set of candidate QTLs must be supplied by the QTLCANDIDATES parameter. The model assumes ENVIRONMENTS (or POPULATIONS) as a fixed term, and GENOTYPES as a random term. Extra fixed effects can be defined using the FIXED option. A multi-Normal distribution is assumed for the random genetic effects, with mean vector 0 and variance-covariance matrix Σ. The VCMODEL option defines the model to use for Σ. See the VGESELECT procedure for details of the available models; the default is to use compound symmetry for multi-environment trials, and diagonal for multiple populations. 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 significance level to use at each step of the backward selection process is given by the ALPHALEVEL option (default 0.05).
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 list of selected QTLs can be saved by the QTLSELECTED parameter, and a logical variate that indicates whether the selected QTL showed a significant QTL-by-environment (or QTL-by-population) interaction can be saved by the INTERACTIONS parameter. This interaction is the combined effect of the ADDITIVEPREDICTORS, ADD2PREDICTORS and DOMINANCEREDICTORS pointers if specified. After the final step of the backward selection, extra tests are performed if the DOMINANCEPREDICTORS parameter is set. If the selected QTL has no interaction effect with environment (or population), a test is performed of whether the dominance effect has a significant contribution in the combined QTL effect. If dominance is significant, the corresponding units of the logical variate saved by the DOMSELECTED parameter are set to one; the other units are set to zero. If the selected QTL has significant interaction with environment (or population), a test is performed of whether the dominance-by-environment (or dominance-by-population) interaction has a significant contribution in the combined QTL-by-environment (or QTL-by-population) interaction. If the dominance-by-environment (or dominance-by-population) interaction is significant, the corresponding units of the logical variate saved by DOMINTERACTIONS parameter are set to one; the other units are set to zero. The Wald test and associated probability values for the combined effects (including the possible not-significant dominance and dominance-by-environment or dominance-by-population interactions) of the selected QTLs can be saved by the WALDSTATISTICS and PRWALD parameters, respectively.
Options: PRINT, POPULATIONTYPE, ALPHALEVEL, VCMODEL, VCPARAMETERS, VCSELECT, CRITERION, FIXED, UNITFACTOR, MVINCLUDE, MAXCYCLE, WORKSPACE.
Parameters: TRAIT, GENOTYPES, ENVIRONMENTS, POPULATIONS, UNITERROR, VCINITIAL, SELECTEDMODEL, ADDITIVEPREDICTORS, ADD2PREDICTORS, DOMINANCEPREDICTORS, CHROMOSOMES, POSITIONS, IDLOCI, IDMGENOTYPES, QTLCANDIDATES, QTLSELECTED, INTERACTIONS, DOMSELECTED, DOMINTERACTIONS, WALDSTATISTICS, PRWALD.
Method
QMBACKSELECT starts with the following mixed models, which include a set L of candidate 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 αjldom ) + 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.
The backward selection procedure starts with the initial set of loci (defined by the QTLCANDIDATES parameter), and checks whether all loci are significant. If not, the locus with the lowest Wald test statistic is dropped from the model. This process is repeated until all loci in the model are significant. The procedure then switches to test whether the remaining QTLs show significant QTL-by-environment (or QTL-by-population) interaction, by breaking down the QTL effects into QTL main effects and QTL-by-environment (or QTL-by-population) interaction effects. If the QTL-by-environment (or QTL-by-population) interaction term is not significant, only a main effect is retained in the model for the corresponding QTL.
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: QMESTIMATE, QMQTLSCAN, QMVAF, VGESELECT.
Commands for: Statistical genetics and QTL estimation.
Example
CAPTION 'QMBACKSELECT 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
" Candidate QTL positions (peaks) from QMQTLSCAN"
VARIATE [VALUES=14...22,40...42,236...240] Qid
" Best variance-covariance model from VGESELECT "
TEXT model; VALUE='fa'
QMBACKSELECT [PRINT=summary,wald; POPULATIONTYPE=F2; ALPHA=0.05;\
VCMODEL=#model] TRAIT=yld; ENVIRONMENTS=E; GENOTYPES=G;\
ADDITIVEPREDICTORS=addpred; DOMINANCEPREDICTORS=dompred;\
QTLCANDIDATES=Qid; CHROMOSOMES=mkchr; POSITIONS=mkpos;\
IDLOCI=idlocus; QTLSELECTED=qtlsel; INTERACTIONS=qtlint;\
DOMSELECTED=domsel; DOMINTERACTIONS=domint; WALDSTAT=stat;\
PRWALD=prwald
PRINT qtlsel,qtlint,domsel,domint; DECIMALS=0