makeMinv {nadiv}

Create the inverse (additive) mutational effects relationship matrix

Description

Returns the inverse of the (additive) mutational effects relationship matrix. It can also be used to obtain components needed for the calculations in the underlying algorithm.

Usage

makeMinv(pedigree, ...)

makeMinvML(pedigree, ...)

Arguments

pedigree

A pedigree where the columns are ordered ID, Dam, Sire

...

Arguments to be passed to methods

Details

Missing parents (e.g., base population) should be denoted by either 'NA', '0', or '*'.

Note the assumption under the infinitesimal model, that mutation has essentially zero probability of affecting an inbred locus (hence removing inbred identity-by-descent), however, mutations may themselves be subject to inbreeding (Wray 1990).

By default, the algorithm described in Casellas and Medrano (2008) is implemented here, in which the inverse-M is separate from the typical inverse relatedness matrix (inverse-A). Casellas and Medrano's algorithm allows separate partitioning of additive genetic variance attributed to inheritance of allelic variation present in the base population (inverse-A) from additive genetic variance arising from mutation and subsequent sharing of mutant alleles identical-by-descent. Alternatively, Wray (1990) formulates an algorithm which combines both of these processes (i.e., the A-inverse with the M-inverse matrices). If the Wray algorithm is desired, this can be implemented by specifying a numeric value to an argument named theta. The value used for theta should be as described in Wray (1990). See examples below for use of this argument.

Value

a list:

Minv

the inverse of the (additive) mutational effects relationship matrix in sparse matrix form

listMinv

the three column list of the non-zero elements for the inverse of the (additive) mutational effects relationship matrix. attr(*, "rowNames") links the integer for rows/columns to the ID column from the pedigree.

h

the amount by which segregation variance is reduced by inbreeding. Similar to the individual coefficients of inbreeding (f) derived during the construction of the inverse numerator relatedness matrix. in the pedigree (matches the order of the first/ID column of the pedigree).

logDet

the log determinant of the M matrix

dii

the (non-zero) elements of the diagonal D matrix of the M=TDT' decomposition. Contains the variance of Mendelian sampling. Matches the order of the first/ID column of the pedigree. Note Wray (1990) and Casellas and Medrano (2008) algorithms use v=sqrt(dii).

Author(s)

[e-mail]

References

Casellas, J. and J.F. Medrano. 2008. Within-generation mutation variance for litter size in inbred mice. Genetics. 179:2147-2155.

Meuwissen, T.H.E & Luo, Z. 1992. Computing inbreeding coefficients in large populations. Genetics, Selection, Evolution. 24:305-313.

Mrode, R.A. 2005. Linear Models for the Prediction of Animal Breeding Values, 2nd ed. Cambridge, MA: CABI Publishing.

Wray, N.A. 1990. Accounting for mutation effects in the additive genetic variance-covariance matrix and its inverse. Biometrics. 46:177-186.

Examples

 ##  Example pedigree from Wray 1990
 #### Implement Casellas & Medrano (2008) algorithm
   Mout <- makeMinv(Wray90[, 1:3])
 #### Wray (1990) algorithm with extra argument `theta`
   Mwray <- makeMinv(Wray90[, 1:3], theta = 10.0)$Minv # compare to Wray p.184