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

- 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

- Compute equilibrium parameters under univariate AM

`rBahadur`

is now on CRAN:

`install.packages("rBahadur")`

Alternatively, you can install directly from github using the
`install_github`

function provided by the `remotes`

library:

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

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

```
set.seed(2022)
= .5; m = 2000; n = 5000; r =.5; min_MAF=.05
h2_0
## simulate genotype/phenotype data
<- am_simulate(h2_0, r, m, n) sim_dat
```

We compare the target and realized allele frequencies:

```
## plot empirical first moments of genotypes versus expectations
<- colMeans(sim_dat$X)/2
afs_emp plot(sim_dat$AF, afs_emp)
```

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

```
## empirical h2 vs expected equilibrium h2
<- var(sim_dat$g)/var(sim_dat$y))
(emp_h2 h2_eq(r, .5)
```

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

- 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

- Teugels, J.L., 1990. Some representations of the multivariate
Bernoulli and binomial distributions.
- 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

- Nagylaki, T., 1982. Assortative mating for a quantitative character.