Rindsel: a R package for Selection Indices S. Perez-Elizalde, J. Crossa, J. Ceron-Rojas, and G. Alvarado Biometrics and Statistics Unit CIMMYT 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).

Selection Index=SI Breeding value SMITH SELECTION INDEX Two basic linear combinations Selection Index=SI Breeding value Phenotypic values Genotypic values Economic weights (constant) Coefficients

ESIM where and are the eigenvalue and eigenvector of , respectively. The selection response is thus maximizing R is equivalent to maximizing the variance of the SI therefore the selection response is

LANDE and THOMPSON where 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 Consider According to BULMER (1980), maximizing is equivalent to maximizing the covariance is invariant to scale changes, it is possible to incorporate two restrictions, and in MESIM and solutions are Since and

Thus, the values that maximize under restrictions are the eigenvalues and eigenvectors of matrix Q

How to install Rindsel Packages lme4 and Hmisc have to be installed 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 >?LTIndex Or 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 the scores and its related marker

7. Finally, the output file is displayed. There are three output files 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)