Efficient simulation of genotype / phenotype data under assortative mating by generating Bahadur order-2 multivariate Bernoulli distributed random variates.

Features

• Multivariate Bernoulli (MVB) distribution samplers
  • rb_dplr: generate Bahadur order-2 MVB variates with diagonal-plus-low-rank (DPLR) correlation structures
  • rb_unstr: generate Bahadur order-2 MVB variates with arbitrary correlation structures
• Assortative mating modeling tools
  • Compute equilibrium parameters under univariate AM
  • h2_eq: compute equilibrium heritability
  • rg_eq: compute equilibrium cross-mate genetic correlation
  • vg_eq: compute equilibrium genetic variance
  • Generate genotype / phenotype data given initial conditions
  • am_simulate: complete univariate genotype / phenotype simulation
  • am_covariance_structure: compute outer-product covariance component for AM-induced DPLR covariance structure

Installation

rBahadur is now on CRAN:

r install.packages("rBahadur")

Alternatively, you can install directly from github using the install_github function provided by the remotes library:

r remotes::install_github("rborder/rBahadur")

Usage

Here we demonstrate using rBahadur to simulate genotype / phenotype at equilibrium under AM: given the following parameters:

• h2_0: panmictic heritability
• r: cross-mate phenotypic correlation
• m: number of diploid, biallelic causal variants
• n: number of individuals to simulate
• min_MAF: minimum minor allele frequency

```r set.seed(2022) h20 = .5; m = 2000; n = 5000; r =.5; minMAF=.05

simulate genotype/phenotype data

simdat <- amsimulate(h2_0, r, m, n) ```

We compare the target and realized allele frequencies:

```r

plot empirical first moments of genotypes versus expectations

afsemp <- colMeans(simdat$X)/2 plot(simdat$AF, afsemp) ```

We compare the expected equilibrium heritability to that realized in simulation:

```r

empirical h2 vs expected equilibrium h2

(emph2 <- var(simdat$g)/var(simdat$y)) h2eq(r, .5) ```

Citation

Developed by Richard Border and Osman Malik. For further details, or if you find this software useful, please cite: - Border, R. and Malik, O.A., 2022. rBahadur: efficient simulation of structured high-dimensional genotype data with applications to assortative mating. BMC Bioinformatics. https://doi.org/10.1186/s12859-023-05442-6

Background reading:

• The Multivariate Bernoulli distribution and the Bahadur representation:
  • Teugels, J.L., 1990. Some representations of the multivariate Bernoulli and binomial distributions. Journal of Multivariate Analysis, 32(2), pp.256-268. https://doi.org/10.1016/0047-259X(90)90084-U
  • Bahadur, R.R., 1959. A representation of the joint distribution of responses to n dichotomous items. School of Aviation Medicine, Randolph AFB, Texas. https://apps.dtic.mil/sti/citations/AD0706093
• Cross-generational dynamics of genetic variants under univariate assortative mating:
  • Nagylaki, T., 1982. Assortative mating for a quantitative character. Journal of Mathematical Biology, 16, pp.57–74. https://doi.org/10.1007/BF00275161