Performs a QTL backward selection for loci in multi-trait trials (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 traits (identity , diagonal , cs , hcs , outside , fa , fa2 , unstructured ); default cs |
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 |
STANDARDIZE = string token |
How to standardize the traits (none , normalize ) ; default norm |
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
Y = variates |
Quantitative traits to be analysed; must be set |
---|---|
GENOTYPES = factors |
Genotype factor; must be set |
FTRAITS = factors |
Factor indicating the trait of each y-value; 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 |
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-trait 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-trait interaction |
WALDSTATISTICS = variates |
Saves the Wald test statistics |
PRWALD = variates |
Saves the associated Wald probabilities |
Description
QMTBACKSELECT
selects QTLs by backward selection from a list of candidate QTLs (loci) in multi-trait trials. It uses means per genotype-trait 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 Y
parameter, and the corresponding trait and genotype factors must be specified by the FTRAITS
and GENOTYPES
parameters, respectively. The POPULATIONTYPE
option must be set to specify the population from which the genotypes have been derived. By default, the values of each trait are standardized by dividing them by their standard deviation, but you can set option STANDARDIZE=none
to suppress this.
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 FTRAITS
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. 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-trait 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 trait, 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 trait, a test is performed of whether the dominance-by-trait interaction has a significant contribution in the combined QTL-by-trait interaction. If the dominance-by-trait 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-trait 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: Y
, GENOTYPES
, FTRAITS
, UNITERROR
, VCINITIAL
, SELECTEDMODEL
, ADDITIVEPREDICTORS
, ADD2PREDICTORS
, DOMINANCEPREDICTORS
, CHROMOSOMES
, POSITIONS
, IDLOCI
, IDMGENOTYPES
, QTLCANDIDATES
, QTLSELECTED
, INTERACTIONS
, DOMSELECTED
, DOMINTERACTIONS
, WALDSTATISTICS
, PRWALD
.
Method
QMTBACKSELECT
starts with the following mixed models, which include a set L of candidate QTLs:
1) yij = μ + Tj + Σl∈L xiladd αjladd + GTij
if only ADDITIVEPREDICTORS
are specified
2) yij = μ + Tj + Σl∈L ( xiladd αjladd + xildom αjldom ) + GTij
if DOMINANCEPREDICTORS
are also specified
3) yij = μ + Tj + Σl∈L ( xiladd αjladd + xiladd2 αjladd2 + xildom αjldom ) + GTij
if both ADD2PREDICTORS
and DOMINANCEPREDICTORS
are specified (for population type CP
)
where yij is the value of trait j for genotype i, Tj is the trait 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). GTij 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-trait interaction, by breaking down the QTL effects into QTL main effects and QTL-by-trait interaction effects. If the QTL-by-trait 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: QMTESTIMATE
, QMTQTLSCAN
, QMVAF
, VGESELECT
.
Commands for: Statistical genetics and QTL estimation.
Example
CAPTION 'QMTBACKSELECT 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 " append the traits " SUBSET [E.EQ.6] G,asi,eno,mflw,ph,yld APPEND [NEWVECTOR=y ; GROUPS=ftraits] asi,eno,mflw,ph,yld APPEND [NEWVECTOR=G] 5(G) " candidate QTL positions from QMTQTLSCAN " VARIATE [VALUES= 17...22, 72,101,102...105, 135...139,\ 153,154,188,189...192,206...210,212...222,\ 227,236,237,238] Qid TEXT model; VALUE='fa' QMTBACKSELECT [PRINT=summary,wald; POPULATIONTYPE=F2; ALPHA=0.05;\ VCMODEL=#model] Y=y; FTRAITS=ftraits; 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