Reacnorm (version 0.2.1)

rn_gamma_env: Compute the \(\gamma\)-decomposition of additive genetic variance per environment

Description

This function computes the \(\gamma\)-decomposition of the additive genetic variance for each environment.

Usage

rn_gamma_env(theta, G_theta, env = NULL, shape = NULL, X = NULL,
             fixed = NULL, width = 10)

Value

This function yields a data.frame containing the input values for the environment, the additive genetic variance in each of them, with its corresponding \(\gamma\)-decomposition (data.frame, all numeric).

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)

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)

Author

Pierre de Villemereuil

Details

This function provides the \(\gamma\)-decomposition (according to each parameter of the reaction norm and their covariances) of the additive genetic variance in each environment.

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.

If X is provided the second column is returned as the value for the "environment" (based on the assumption that a polynomial function was used).

See Also

rn_vgen, rn_gen_decomp

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

# 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_gamma_env(theta   = theta,
             G_theta = G,
             X       = X)