Reacnorm (version 0.2.1)

rn_pi_decomp: Compute the \(\pi\)-decomposition of \(V_{\text{Plas}}\)

Description

This function calculates the plastic variance of the average (over genotypes) reaction norm shape \(V_{\text{Plas}}\) and its \(\pi\)-decomposition into \(\pi_{\text{Sl}}\) and \(\pi_{\text{Cv}}\).

Usage

rn_pi_decomp(theta, V_theta, env, shape, fixed = NULL, wt_env = NULL,
             correction = FALSE, width = 10)

Value

This function yields the \(\pi\)-decomposition of \(V_{\text{Plas}}\) as a one-row data.frame (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)

V_theta

Full 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).

fixed

If some parameters of shape, included in theta are not included in the V_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)

correction

Should Bessel's correction (dividing the sum-of-squares by N-1 rather than N) be used (TRUE) or not (FALSE, default). The default is FALSE, because it is likely that other components such as the total phenotypic variance is computed over the number of individuals (generally large number) rather than the number of environments (generally small number). The best is to manually use Bessel's correction over the proper number of data points. (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)

Author

Pierre de Villemereuil

Details

The variance \(V_{\text{Plas}}\) is the variance arising from the shape of the reaction norm after averaging over the genetic variance, i.e. the purely environmental part of the variance of plasticity in the reaction norm. Its \(\pi\)-decomposition into a slope (\(\pi_{\text{Sl}}\)) and curvature (\(\pi_{\text{Cv}}\)) components allows to distinguish the importance of each of those components in \(V_{\text{Plas}}\). Note that the \(\pi\)-decomposition requires that the environmental variable is normally distributed, or that the reaction norm shape is quadratic.

It is very important that the parameters are in the same order in theta (which, again, must be named) and in V_theta.

See Also

rn_mean_by_env, rn_vplas

Examples

# Some environment vector
vec_env <- rnorm(20)

# 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 the pi-decomposition of V_Plas
rn_pi_decomp(theta   = theta,
             V_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 to the environmental values according to a normal distribution
# if the env variable is actually fixed
vec_env2 <- seq(-2, 2, length.out = 20)
rn_pi_decomp(theta   = theta,
              V_theta = G,
              env     = vec_env2,
              shape   = expr,
              fixed   = c(3, 4),
              wt_env  = dnorm(vec_env2))