makeD {nadiv}

Create the dominance genetic relationship matrix

Description

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.

Usage

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
)

Arguments

pedigree

A pedigree with columns organized: ID, Dam, Sire. For use with makeSd, a fourth column indicates the sex of each individual in the pedigree.

parallel

Logical, indicating whether computation should be run on multiple processors at once. See details for considerations.

ncores

Number of cores to use when parallel = TRUE. Default is maximum available. Otherwise, set with an integer. See details for considerations.

invertD, invertSd

A logical indicating whether or not to invert the D or S matrix

returnA, returnS

Logical, indicating if the numerator relationship matrix (A or S) should be stored and returned.

det

Logical, indicating if the determinant of the D or Sd matrix should be returned.

verbose

Logical, indicating if progress messages should be displayed.

heterogametic

Character indicating the label corresponding to the heterogametic sex used in the "Sex" column of the pedigree

DosageComp

A character indicating which model of dosage compensation. If NULL then the “ngdc” model is assumed.

Details

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.

Value

a list:

A,S

the A or S matrix in sparse matrix form

D,Sd

the D or Sd matrix in sparse matrix form

logDet

the log determinant of the D or Sd matrix

Dinv,Sdinv

the inverse of the D or inverse of the Sd matrix in sparse matrix form

listDinv,listSdinv

the three column form of the non-zero elements for the inverse of the D or the inverse of the Sd matrix

Author(s)

[e-mail]

References

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.

See Also

makeDsim, makeSdsim

Examples

  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