There is an option (originally included in REMLF90 by Miguel Perez Enciso) included to include covariance structures, say T, computed from outside. This covariance structures will be included in the mixed model equations for the corresponding random effect. This option works in all programs (BLUP, REML, Gibbs… ).

This is useful in several cases, including for example:

1. plant breeding (with tetra or hexa-ploids or self-fertilization),
2. uncertain parentships,
3. kernel methods such as RKHS,
4. genomic relationship matrices (although the latter are correctly included using genomic options)
5. autoregressive covariance structures.

The inclusion is rather simple. One has to include a random effect of the type, either

• user_file if the file contains the inverse of the covariance structure, that is, it contains T^-1 ,
• user_file_inv if the file contains the covariance structure, that is, it contains T. If this is the case, T is inverted (Not implemented in the IOD programs),

and declare a file (in this example, Gi) with the covariance structure:

RANDOM_GROUP
 # genomic
 2
RANDOM_TYPE
user_file
FILE
 # matrix file
Gi

The file has to have the form (row, col, value) in Ascii (i.e. plain text), stored as lower- or upper- triangle, e.g., this is valid:

1 1 1
1 2 0.5
2 2 1

but this is not valid:

1 1 1
1 2 0.5
2 1 0.5
2 2 1

Elements of T not stored in the file are assumed to be zero. Therefore, the file with the covariance structure is not necessarily very large . For instance, matrix

1.0  0.0  0.5
0.0  0.5  0.0
0.5  0.0  1.1

can be stored as:

1 1 1.0
1 3 0.5
2 2 0.5
3 3 1.1