Rindsel: a R package for Selection Indices

S. Perez-Elizalde, J. Crossa, J. Ceron-Rojas, and G. Alvarado

Biometrics and Statistics UnitCIMMYT

and Colegio de Postgraduado, Montecillos, Edo. de Mexico,

Mexico

SELECTION INDICES (SI)Phenotypic selection indices

• Smith selection index• Restrictive Kempthorne & Nordskog selection index• Eiegen Selection Index Method• Restrictive eigen selection index method

Molecular selection indices

• Lande and Thompson (1990) molecular SI.

• Molecular ESIM (Ceron-Rojas et al., 2008).

pβYSI gθZ

SMITH SELECTION INDEXTwo basic linear combinations

][ 1 qp...pp

]...[ 1 qβ

Breeding valueSelection Index=SI

Phenotypic values

Coefficients

]...[ 1 qggg Genotypic values

]...[ 1 qθ Economicweights (constant)

ESIM

0βIS )(

where and are the eigenvalue and eigenvector of , respectively. β S

The selection response is thus maximizing R is

equivalent to maximizing the variance of the SI therefore

the selection response is ΣθΣSθ 1ˆ kR

Sββk

R̂

Sββ

LANDE and THOMPSON

mβpβ mpMY

m

pββ mp

Nmm ...1mwhere each mj (j=1, 2, …, N; N= number of molecular scores) is the sum of the products of the MQTL effects multiplied by the coded values of their corresponding MM

MESIM

MMMMMM

MMMMZYMM kkR

MM βSβθΣθ

βΣθ

Consider

MMM βΣθ

According to BULMER (1980), maximizing is equivalent to

maximizing the covariance

MM ZY

Since is invariant to scale changes, it is possible to incorporate

two restrictions, and in MESIM

and solutions are

MM ZY

1MMM βSβ 1

MMM θΣθ

0βIQ

0βIΣS

M

MMM

)(

)(2

21

MMMM βSΣθ 1 and

0βIQ

0βIΣS

M

MMM

)(

)(2

21

Thus, the values that maximize under restrictions

are the eigenvalues

and eigenvectors of matrix Q

MMM βΣθ

1MMM βSβ 1

MMM θΣθ

MβMMM βΣθ

How to install Rindsel

1) Packages lme4 and Hmisc have to be installed2) From the menu Packages select install package(s)

from local zip file …

2) Select the file Rindsel_1.0.zip from the directory where is located

Help for Rindsel

• From the menu help of R call the html help browser

• Select the link packages and search for Rindsel

• Or, type help.search() in the R commad promt

Load Rindsel• From the Packages menu select Load Package.

Available packages are displayed. Select Rindsel• Now, you can use the functions of the package. On the command prompt, write IndexName() to display the main menu

Lande and Thompon Selection Index

For help about the Lande and Thompson selection index funtion, on the R command prompt write>?LTIndexOr use the htlm help browser

Example: Lande & Thompson

2. On the R command line or in a script write LTIndex()

if you execute the function without arguments as above defaults options will be used

3. A window will automatically open requesting the phenotypic data file (field desig and entry x trait responses). Browse the selected file.

4. Next browse the weigths file

In the firs column of the spreadsheet are the traits names, the second the indicator variable o the selected traits, the third one the economic weights (LTIndex) and the fourth one the desired effect of selection (MESIMIndex)

The R routine begins to calculate de genetic and phenotypic covariance (correlation) matrices.5. After finished the calculation a window will request for the markers file

Select the file and browse it

6. Browse the molecular scores file

The file contains thescores and its related marker

7. Finally, the output file is displayed. There are three output files. A plain text file which contains the selected traits, a copy of this file in csv format is also generated. A third file contains all the traits and their selection index values.

For the MESIM selection index we proceed in the same way. Example: select the 10 percent of traits with the highest values of the MESIM index. Use covariance matrices already calculated. MESIMIndex(selval=10, rawdata=FALSE)