rn_vgen: Compute the total genetic variance V_{\text{Gen}}

In Reacnorm: Perform a Partition of Variance of Reaction Norms

Compute the total genetic variance V_{\text{Gen}}

Description

This function calculates the total genetic variance V_{\text{Gen}} arising from genetic variation in the reaction norm.

Usage

rn_vgen(theta, G_theta, env = NULL, shape = NULL, X = NULL, fixed = NULL, wt_env = NULL,
        average = TRUE, width = 10)

Arguments

theta	Average parameters of the shape function. It must be a named vector, with the names corresponding to the parameters in the shape expression. (numeric)
G_theta	Genetic variance-covariance matrix of the parameters. It can be of lesser dimensions than theta, see fixed parameter. (numerical matrix)
env	Vector of environmental values (numeric).
shape	Expression providing the shape of the reaction where x is the environment. For example: expression(a + b * x + c * x^2).
X	If the model used was linear in the parameters, the design matrix X of the model (numeric, incompatible with the arguments env and shape).
fixed	If some parameters of shape, included in theta are not included in the G_theta matrix, then those dimensions are considered as genetically "fixed". Hence, fixed should contain a vector of the index of those parameters. Otherwise (if all parameters vary genetically), and by default, fixed should be set as NA. (integer)
wt_env	Weights to apply to the env vector values, providing an information regarding their relative probability in the biological context. The weights must non-negative, and at least one must non-zero. The vector wt_env must be the same length as env. By default, no weighting is applied. (numeric)
average	Should the values for each environment be given, or just their average (default)? (boolean)
width	Parameter for the integral computation. The integral is evaluated from mu - width * sqrt(var) to mu + width * sqrt(var). The default value is 10, which should be sensible for most models. (numeric)

Details

The variance V_{\text{Gen}} is the total genetic variance in the reaction norm. If the reaction norm is linear in its parameters, then is it also equal to the total additive genetic variance in the reaction norm (V_{\text{Add}}). Otherwise, see the function rn_gen_decomp to compute V_{\text{Add}}.

It is very important that the parameters are in the same order in the argument of the shape function, in theta and in G_theta.

Value

This function yields the genetic variance arising from all the genetic variation in the reaction norm (numeric).

Author(s)

Pierre de Villemereuil

See Also

rn_gen_decomp, rn_vplas, rn_vtot

Examples

# Some environment vector
vec_env <- seq(-2, 2)

# Shape function
expr <- expression(
     cmax * exp(
         - exp(rho * (x - xopt) - 6) -
             sigmagaus * (x - xopt)^2
     ))

# Theta
theta <- c(cmax = 1, xopt = 0.9, rho = 8, sigmagaus = 0.4)
# G, only for cmax and xopt
G     <- matrix(c(0.1,      0.01,
                  0.01,     0.05),
                ncol = 2)

# Computing V_gen
rn_vgen(theta   = theta,
        G_theta = G,
        env     = vec_env,
        shape   = expr,
        fixed   = c(3, 4))
# Note that fixed is set for the third and forth parameters than are not in G

# Applying some weighting according to a normal distribution
rn_vgen(theta   = theta,
        G_theta = G,
        env     = vec_env,
        shape   = expr,
        fixed   = c(3, 4),
        wt_env  = dnorm(vec_env))

# Setting average to FALSE allows to obtain the value for each environment
rn_vgen(theta   = theta,
        G_theta = G,
        env     = vec_env,
        shape   = expr,
        fixed   = c(3, 4),
        average = FALSE)

# If a polynomial was used, it is possible to use the linear modeling rather having
# to compute integrals
theta <- c(a = 1.5, b = 0.5, c = -0.5)
X     <- cbind(1, vec_env, (vec_env - mean(vec_env))^2)
G     <- 0.1 * diag(3)
rn_vgen(theta   = theta,
        G_theta = G,
        X       = X)
# Should be very close to the computation with integration
rn_vgen(theta   = theta,
        G_theta = G,
        env     = vec_env,
        shape   = expression(a + b * x + c * x^2))

Reacnorm documentation built on April 3, 2025, 9:24 p.m.