Reacnorm (version 0.2.1)

rn_vp_env: Compute the total phenotypic variance \(V_{\text{Tot}}\)

Description

This function calculates the total phenotypic variance \(V_{\text{Tot}}\) arising along and beyond the reaction norm, i.e. including the residual variance.

Usage

rn_vp_env(theta, V_theta, var_res, env = NULL, shape = NULL, X = NULL,
          fixed = NULL, wt_env = NULL, width = 10)

Value

This function yields the phenotypic variance in each environment (numerical vector).

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)

V_theta

Full variance-covariance matrix of the parameters. It can be of lesser dimensions than theta, see fixed parameter. (numerical matrix)

var_res

Residual variance beyond the reaction norm. It could be a scalar if this residual variance is assumed homogeneous or a vector the same length as env (or number of rows of X), if the residual variance is allowed to vary across the environment. (numeric scalar or vector)

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)

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

The phenotypic variance at a given environment depends on the variation in the \(\theta\) parameters and the residual variance. It thus account for everything but the variance due to the average shape of the reaction norm (i.e. \(V_{\text{Plas}}\)).

See Also

rn_vplas, rn_vgen

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)
# Another covariance matrix for cmax and xopt (e.g. permanent environment, or maternal effet)
M     <- matrix(c(0.05,      0,
                  0,      0.01),
                ncol = 2)
# Full variance-covariance matrix
P     <- G + M
# Residual variance
vr    <- 0.1
                
# Computing V_tot
rn_vp_env(theta   = theta,
          V_theta = P,
          var_res = vr,
          env     = vec_env,
          shape   = expr,
          fixed   = c(3, 4))
# Note that fixed is set for the third and forth parameters than are not in P