am_equilibrium_parameters {rBahadur}

Functions to compute equilibrium parameters under assortative mating

Description

Compute heritability ('h2_eq'), genetic variance ('vg_0'), and cross-mate genetic correlation ('rg_eq') at equilibrium under univariate primary-phenotypic assortative mating. These equations can be derived from Nagylaki's results (see below) under the assumption that number of causal variants is large (i.e., taking the limit as the number of causal variants approaches infinity).

Usage

h2_eq(r, h2_0)

rg_eq(r, h2_0)

vg_eq(r, vg_0, h2_0)

Arguments

r

cross-mate phenotypic correlation

h2_0

generation zero (panmictic) heritability

vg_0

generation zero (panmictic) additive genetic variance component

Value

A single numerical quantity representing the equilibrium heritability (h2_eq), the equilibrium cross-mate genetic correlation (rg_eq), or the equilibrium genetic variance (vg_eq).

References

Nagylaki, T. Assortative mating for a quantitative character. J. Math. Biology 16, 57–74 (1982). https://doi.org/10.1007/BF00275161

Examples

set.seed(1)
vg_0= .6; h2_0 = .5; r =.5
h2_eq(r, h2_0)
rg_eq(r, h2_0)
vg_eq(r, vg_0, h2_0)