Simulate a genomic data set

Draws biallelic marker genotypes, forms the genomic relationship matrix of VanRaden (2008), and simulates a trait with the requested heritability, so that reml_sketch() can be checked against known variance components.

Usage

sim_genomic(
  n = 1000L,
  p = 2000L,
  h2 = 0.5,
  pops = 1L,
  fst = 0.05,
  form_G = TRUE
)

Arguments

n: Number of individuals.
p: Number of markers.
h2: Heritability, between 0 and 1.
pops: Number of subpopulations.
fst: Fixation index between subpopulations, used when pops > 1.
form_G: Return the relationship matrix itself. Set to FALSE for large n and pass grm_matrix(M) to the fitting functions instead.

Value

A list with the phenotype y, an intercept design matrix X, the genotype matrix M, the relationship matrix G (when form_G = TRUE), the subpopulation of each individual pop, and the true h2.

Details

With pops > 1 the individuals come from that many subpopulations whose allele frequencies have drifted apart under the Balding-Nichols model with fixation index fst. Population structure gives the relationship matrix a few large eigenvalues, as real breeding and human cohorts do, and those are exactly what a low-rank preconditioner captures.

Genetic values are sums of marker effects on the centred genotypes, with variance chosen so that the genetic and residual variance components on the scale of the relationship matrix are h2 and 1 - h2.

The function draws random numbers but does not set the seed; call base::set.seed() first for a reproducible data set.

References

VanRaden, P. M. (2008) Efficient methods to compute genomic predictions. Journal of Dairy Science 91, 4414-4423. doi:10.3168/jds.2007-0980

Balding, D. J. & Nichols, R. A. (1995) A method for quantifying differentiation between populations at multi-allelic loci and its implications for investigating identity and paternity. Genetica 96, 3-12. doi:10.1007/bf01441146

Examples

set.seed(1)
dat <- sim_genomic(n = 200, p = 500, h2 = 0.4, pops = 3)
dim(dat$G)
#> [1] 200 200
table(dat$pop)
#> 
#>  1  2  3 
#> 67 67 66