### molecular_selection_index_methods

```Rindsel: a R package for Selection Indices
S. Perez-Elizalde, J. Crossa, J. Ceron-Rojas, and G.
Biometrics and Statistics Unit
CIMMYT
and
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).
SMITH SELECTION INDEX
Two basic linear combinations
Selection Index=SI
SI  Y  β p
p   [ p1
...
β   [ 1
...
p q ] Phenotypic values
 q ] Coefficients
Breeding value
Z  θ g
g  [ g1
...
θ   [ 1
...
g q ] Genotypic
q]
values
Economic
weights
(constant)
ESIM
(S   I )β  0
where  and β are the eigenvalue and eigenvector of S , respectively.
k
ˆ
The selection response is R 

β S β thus maximizing R is
equivalent to maximizing the variance of the SI β S β therefore
the selection response is Rˆ  k θ ΣS
1
Σθ
LANDE and THOMPSON
Y M  β p p  β m m  β p
m   m1
...
mN 
β m


p
 
m 
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
RM  k M  YM Z M  k M
θ M Σ M β M
θ M Σ M θ M
β M S M β M
According to BULMER (1980), maximizing  Y M Z M is equivalent to
maximizing the covariance θ  Σ β
M
M
M
Since  Y M Z M is invariant to scale changes, it is possible to incorporate
two restrictions, β M S M β M  1 and θ M Σ M θ M  1 in MESIM
and solutions are
1
M
θ M   Σ S M β M and
1
M
(S Σ M   I )β M  0
2
(Q   I )β M  0
2
1
M
(S Σ M   I )β M  0
2
(Q   I )β M  0
2
Thus, the values that maximize θ M Σ M β M under restrictions
β M S M β M  1 θ M Σ M θ M  1 are the eigenvalues
  θ M Σ M β M and eigenvectors β M of matrix Q
How to install Rindsel
1) Packages lme4 and Hmisc have to be installed
2) 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
Available packages are
displayed. Select Rindsel
• Now, you can use the functions
of the package. On the command
prompt, write IndexName() to
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. 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
MESIMIndex(selval=10, rawdata=FALSE)
```