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  2. QSELECTIONINDEX procedure


Calculates (molecular) selection indexes by using phenotypic information and/or molecular scores of multiple traits (M. Malosetti & F.A. van Eeuwijk).


PRINT = string tokens What to print (summary); default summ
METHOD = string token Defines which index to calculate (simple, smithhazel, landethompson); default smit
INTENSITY = scalar Specifies the selection intensity expressed as the percentage of individuals of the population to select; default 10


TRAITS = pointers Pointer with a variate for each trait, supplying the phenotypic values for the genotypes; must be set
MOLECULARSCORES = pointers Pointer with a variate for each trait, supplying QTL-based predictions or genomic predictions
GENOTYPES = factors Genotype factor; must be set
IDMGENOTYPES = texts Labels of the genotypes
WEIGHTS = variates Specifies economic weights for the traits; if unset, all traits have weight one
VCPHENOTYPIC = symmetric matrices Specifies the phenotypic variance-covariance matrix of the traits
VCGENETIC = symmetric matrices Specifies the genotypic variance-covariance matrix of the traits
HERITABILITY = symmetric matrices Specifies the heritabilities and coheritabilities of the traits
SELECTIONINDEX = variates Saves the selection index


Selection indexes are a classical tool used in plant and animal breeding to select multiple traits simultaneously, conditional on given economic weights and specific selection targets. QSELECTIONINDEX allows several types of selection index to be calculated, that combine economic weights with additional selection constraints. It can produce standard selection indexes based on phenotypic information, or molecular selection indexes by incorporating molecular scores of genotypes derived from QTL or genomic prediction models.

The METHOD option defines which selection index to obtain, either a simple index, the Smith-Hazel index (default), or the Lande and Thompson index. See the Method Section below for details.

The INTENSITY option specifies the desired selection intensity, which is used to calculate the selection differential and the expected response to selection. It also determines the percentage of top performing genotypes to be to printed.

The TRAITS parameter must supply the phenotypes (observations) of the individuals whose selection indexes are to be calculated. Alternatively, you can use it to specify molecular scores (predictions from a QTL or genomic prediction model) if you want to construct an index based only on these. However, the Lande and Thompson index needs both phenotypes and molecular scores, and then the MOLECULARSCORES parameter must be used to supply the molecular scores of the individuals, while the TRAITS parameter provides the phentoypes.

The GENOTYPES parameter must specify a factor to identify the individuals, and the IDMGENOTYPES parameter can supply a text to label the genotypes.

The WEIGHTS parameter specifies the economic weights to use for each of the traits entering the index. These must be given in the same order as in the pointer supplied by the TRAITS and MOLECULARSCORES parameters. The default is to use a weight of one for every trait.

The VCPHENOTYPIC and VCGENETIC parameters can be used to provide the phenotypic and genetic variance-covariance matrices between the traits. The rows of the matrices correspond to the traits, and must follow the same order as in the TRAITS and MOLECULARSCORES pointers. If VCPHENOTYPIC and VCGENETIC are not specified, the HERITABILITY parameter must be specified instead, to define the heritabilities and coheritabilities of the traits, is a symmetric matrix with the rows must be in the same order as in the TRAITS and MOLECULARSCORES pointers.

The SELECTIONINDEX parameter can be used to save the values of the selection index, in a variate.

By default, QSELECTIONINDEX prints a summary of the analysis, but you can set option PRINT=* to suppress this.




The simple selection index uses either phenotypic information or molecular scores, and is defined as

SI = Y d

where Y is the n×t matrix containing the phenotypic data or the molecular scores for the n genotypes and t traits (with no missing values), and where d is the t×1 vector of trait-specific economic weights.

The Smith-Hazel index also uses either phenotypic information or molecular scores. Its definition is

SH = Y P-1 G d

where P and G are the t×t phenotypic and genotypic variance-covariance matrices.

The Lande and Thompson index uses both phenotypic and molecular scores, and is defined as

LT = Y* P*-1 G* d*

where the matrix Y* combines the matrix of phenotypic trait data Y and the matrix of predictions from the QTL or genomic prediction model (molecular scores) Ym, appended one below the other i.e.

Y =   ( Y )

( Ym )

The corresponding variance-covariance matrices are

P* =  ( P Pm )

( Pm Pm )


G* =   ( G Gm )

( Gm Gm )

where Pm and Gm are the variance-covariance matrices for the molecular scores. The economic weights are

 d* =  ( d )

( 0m )

where 0m is a vector of zero weights for the molecular scores.

Action with RESTRICT

Restrictions are not allowed.

See also


Commands for: Statistical genetics and QTL estimation.


IMPORT    [PRINT=*] '%gendir%/examples/QSEL.csv'; ISAVE=v
TEXT      [VALUES='trait1','trait2','trait3'] traits
SYMMETRIC [ROWS=traits; VALUES=12.856,-0.323,0.929,2.457,0.346,1.503] Gmat
SYMMETRIC [ROWS=traits; VALUES=74.491,-0.321,1.281,2.005,0.388,2.698] Pmat
" collect traits vectors and molecular scores in pointers "
POINTER   [VALUES=v[2...4]] t
POINTER   [VALUES=v[5...7]] ms
" define economic weights "
VARIATE   [VALUES=1,-2.5,0.5] w
" calculate simple, SmithHazel, and LandeThompson indexes "
                WEIGHTS=w; VCPHENOTYPIC=Pmat; VCGENETIC=Gmat;\
                WEIGHTS=w; VCPHENOTYPIC=Pmat; VCGENETIC=Gmat;\
                GENOTYPES=Genotype; WEIGHTS=w; VCPHENOTYPIC=Pmat;\
                VCGENETIC=Gmat; SELECTIONINDEX=SI_lt
Updated on March 6, 2019

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