Given a pedigree, the matrix of coefficients of fraternity are returned - the D matrix for autosomes and the Sd matrix for sex chromosomes. Note, inbreeding is not directly incorporated into the calculation of the coefficients (see Details). Functions will return the inverses of the D and Sd matrices by default, otherwise this operation can be skipped if desired.
makeD(
pedigree,
parallel = FALSE,
ncores = getOption("mc.cores", 2L),
invertD = TRUE,
returnA = FALSE,
det = TRUE,
verbose = TRUE
)makeSd(
pedigree,
heterogametic,
DosageComp = c(NULL, "ngdc", "hori", "hedo", "hoha", "hopi"),
parallel = FALSE,
ncores = getOption("mc.cores", 2L),
invertSd = TRUE,
returnS = FALSE,
det = TRUE,
verbose = TRUE
)
a list:
the A or S matrix in sparse matrix form
the D or Sd matrix in sparse matrix form
the log determinant of the D or Sd matrix
the inverse of the D or inverse of the Sd matrix in sparse matrix form
the three column form of the non-zero elements for the inverse of the D or the inverse of the Sd matrix
A pedigree with columns organized: ID, Dam, Sire. For use
with makeSd, a fourth column indicates the sex of each individual in
the pedigree.
Logical, indicating whether computation should be run on multiple processors at once. See details for considerations.
Number of cores to use when parallel = TRUE. Default is maximum available. Otherwise, set with an integer. See details for considerations.
A logical indicating whether or not to invert the D or S matrix
Logical, indicating if the numerator relationship matrix (A or S) should be stored and returned.
Logical, indicating if the determinant of the D or Sd matrix should be returned.
Logical, indicating if progress messages should be displayed.
Character indicating the label corresponding to the heterogametic sex used in the "Sex" column of the pedigree
A character indicating which model of dosage compensation.
If NULL then the “ngdc” model is assumed.
Missing parents (e.g., base population) should be denoted by either 'NA', '0', or '*'.
There exists no convenient method of obtaining the inverse of the dominance
genetic relatedness matrix (or the D matrix itself) directly from a pedigree
(such as for the inverse of A, i.e., Quaas (1995)). Therefore, these
functions computes the coefficient of fraternity (Lynch and Walsh, 1998) for
every individual in the pedigree with a non-zero additive genetic
relatedness in the case of autosomes (makeD) or for the homogametic
sex only in the case of sex chromosomes (makeSd, because the
heterogametic sex has only one copy of the shared sex chromosome and
therefore cannot express dominance allelic interactions).
The coefficients of fraternity are only approximations that assume no inbreeding. The algorithm used here, however, incorporates inbreeding into the calculation of coefficients of coancestry (using `makeA()`) that are used to calculate coefficients of fraternity. Similarly, the diagonals of the D and Sd matrices are corrected for inbreeding. Meaning, the diagonals of D and Sd are (1-f) so that the overall dominance genetic variance is equal to (1-f)V_D, where f is the coefficient of inbreeding and V_D is dominance genetic variance. This is interpreted as the amount of dominance genetic variance that would be expected if the allele frequencies in the inbred population were representative of a non-inbred, randomly mating population (Shaw et al. 1998; Wolak and Keller 2014). Note, the construction of the D matrix is more computationally demanding (in computing time and space requirements) than is the construction of A. This is possibly also the case for construction of Sd in comparison to the S matrix.
To overcome the computational difficulties, this function can enable
parallel processing (see package parallel included in the R
distribution) to speed up the execution. Note this is not be possible on
Windows (See parallel documentation for further information),
therefore parallel = TRUE should only be used on Linux or Mac
operating systems (i.e., not Windows). The default is to use the maximum
number of cpus available to the machine, but this can be restricted by
indicating the number desired in the argument ncores. Setting up the
multi-processing takes some overhead, so no real advantage is gained for
small pedigrees. Also, since all processes are sharing a fixed amount of
RAM, very large pedigrees using many processes in parallel may not be
feasible due to RAM restrictions (i.e., if each process needs "n" amount of
RAM to run, then ncores should be set to = total RAM/n). Otherwise
the machine can become overworked.
Note, for very large pedigrees returnA or returnS should be
set to FALSE to avoid drastically increasing the memory requirements while
making D or Sd, respectively. When this occurs, 'NULL' is returned for the
element of 'A' in the output of makeD or for the element of 'S' in
the output of makeSd.
Quaas, R.L. 1995. Fx algorithms. An unpublished note.
Lynch M., & Walsh, B. 1998. Genetics and Analysis of Quantitative Traits. Sinauer, Sunderland, Massachusetts.
Shaw, R.G., D.L. Byers, and F.H. Shaw. 1998. Genetic components of variation in Nemophila menziesii undergoing inbreeding: Morphology and flowering time. Genetics. 150:1649-1661.
Wolak, M.E. and L.F. Keller. 2014. Dominance genetic variance and inbreeding in natural populations. In Quantitative Genetics in the Wild, A. Charmantier, L.E.B. Kruuk, and D. Garant eds. Oxford University Press, pp. 104-127.
makeDsim, makeSdsim
DinvMat <- makeD(Mrode9, parallel = FALSE)$Dinv
SdinvMat <- makeSd(FG90, heterogametic = "0", parallel = FALSE)$Sdinv
# Check to make sure getting correct elements
## `simPedDFC()` for pedigree with 4 unique sex-linked dominance relatedness values
uSdx <- unique(makeSd(simPedDFC(3), heterogametic = "M", returnS = FALSE)$Sd@x)
stopifnot(all(uSdx %in% c(1, 0.5, 3/16, 1/16))) #<-- must match one of these 4
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