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

### Options

`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 |

### Parameters

`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 |

### Description

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.

Options: `PRINT`

, `METHOD`

, `INTENSITY`

.

Parameters: `TRAITS`

, `GENOTYPES`

, `IDMGENOTYPES`

, `MOLECULARSCORES`

, `WEIGHTS`

, `VCPHENOTYPIC`

, `VCGENETIC`

, `HERITABILITY`

, `SELECTIONINDEX`

.

### Method

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) *Y _{m}*, appended one below the other i.e.

*Y* = ( *Y* )

( *Y _{m}* )

The corresponding variance-covariance matrices are

*P*^{*} = ( *P * *P _{m}* )

( *P _{m}*

*P*)

_{m}and

*G*^{*} = ( *G * *G _{m}* )

( *G _{m}*

*G*)

_{m}where *P _{m}* and

*G*are the variance-covariance matrices for the molecular scores. The economic weights are

_{m}* d*^{*} = ( *d* )

( 0* _{m}* )

where 0* _{m}* is a vector of zero weights for the molecular scores.

### Action with `RESTRICT`

Restrictions are not allowed.

### See also

Procedure: `QBESTGENOTYPES`

.

Commands for: Statistical genetics and QTL estimation.

### Example

CAPTION 'QSELECTIONINDEX example'; STYLE=meta 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 " QSELECTIONINDEX [METHOD=simple; INTENSITY=5] t; GENOTYPES=Genotype;\ WEIGHTS=w; VCPHENOTYPIC=Pmat; VCGENETIC=Gmat;\ SELECTIONINDEX=SI_s QSELECTIONINDEX [METHOD=SmithHazel; INTENSITY=5] t; GENOTYPES=Genotype;\ WEIGHTS=w; VCPHENOTYPIC=Pmat; VCGENETIC=Gmat;\ SELECTIONINDEX=SI_sh QSELECTIONINDEX [METHOD=LandeThompson; INTENSITY=5] t; MOLECULARSCORES=ms;\ GENOTYPES=Genotype; WEIGHTS=w; VCPHENOTYPIC=Pmat;\ VCGENETIC=Gmat; SELECTIONINDEX=SI_lt