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  2. QSBACKSELECT procedure


Performs a QTL backward selection for loci in single-environment trials (M.P. Boer, M. Malosetti, S.J. Welham & J.T.N.M. Thissen).


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
FIXED = formula Formula with 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
UNITERROR = variates Uncertainty on trait means (derived from individual unit or plot error) to be included in QTL analysis; default * i.e. omitted
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; must be set
DOMSELECTED = variates Logical indicator variable storing one where the selected QTLs show a significant effect of the dominance predictor, zero otherwise
WALDSTATISTICS = variates Saves the Wald test statistics
PRWALD = variates Saves the associated Wald probabilities


QSBACKSELECT selects QTLs from a list of candidate QTLs (loci) in single-environment trials by backward selection. It uses single observation per genotype as phenotypic data. The response variable must be specified by the TRAIT parameter, and the genotypes by the GENOTYPES parameter. The POPULATIONTYPE option must be set to specify the population from which the genotypes are derived.

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 using the DOMINANCEPREDICTORS parameter to specify dominance genetic predictors (e.g. in a F2 population); again they are stored in variates and supplied in a pointer. 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 genotypes as random and QTLs as fixed effects. Extra fixed effects can be defined using the FIXED option. 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. If the dominance predictors have been specified, the DOMSELECTED parameter can save a logical indicator variate storing one where the selected QTLs show a significant effect of the dominance predictor, and zero otherwise. The Wald test and associated probability values for the selected QTLs can be saved by the WALDSTATISTICS and PRWALD parameters, respectively.




QSBACKSELECT starts with one of the following models which includes a set L of candidate QTLs:

1)       yi = μ + ΣlL xiladd αladd + Gi

if only ADDITIVEPREDICTORS are specified

2)       yi = μ + ΣlL ( xiladd αladd + xildom αldom ) + Gi

if DOMINANCEPREDICTORS are also specified

3)       yi = μ + ΣlL ( xiladd αladd + xiladd2 αladd2 + xildom αldom ) + Gi

if both ADD2PREDICTORS and DOMINANCEPREDICTORS are specified (for population type CP)

where yi is the trait value of genotype i, xiladd are the additive genetic predictors of genotype i for locus l, and αadd are the associated effects. In models 2 and 3, xildom are the dominance genetic predictors, and αladd 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 αadd and αadd2 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). Gi is the residual unexplained genetic and environmental variation, which is assumed to follow a Normal distribution with mean 0 and variance σ2.

The backward selection process starts with the initial set of loci L (defined by the QTLCANDIDATES parameter), and checks whether all the loci are significant. If not, the locus with the smallest Wald test statistic is dropped from the model. The process is repeated until all loci in the model are significant. If model 2 or 3 is specified, a further step of model reduction is performed by checking, for each of the remaining loci, whether the dominance effects can be dropped from the model.

Action with RESTRICT

Restrictions are not allowed.


Lynch, M. & Walsh, B. (1998). Genetics and Analysis of Quantitative Traits. Sinauer Associates, Sunderland, MA.

See also


Commands for: Statistical genetics and QTL estimation.


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'
" create single environment "
SUBSET       [E.EQ.6] G,yld
" candidate QTL positions from QSQTLSCAN "
VARIATE      [VALUES=18,19,111,112,236,237] Qid
QSBACKSELECT [PRINT=summary,model,components,effects,monitoring,vcovariance,\            
             deviance,waldtests; POPULATIONTYPE=F2; ALPHA=0.10]\ 
             TRAIT=yld; GENOTYPES=G;\
             CHROMOSOMES=mkchr; POSITIONS=mkpos; QTLCANDIDATES=Qid;\ 
             QTLSELECTED=qtlsel; DOMSELECTED=domsel
PRINT        qtlsel,domsel; DECIMALS=0
Updated on March 6, 2019

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