rn_gen_decomp: Compute the decomposition of the additive genetic variance...
In Reacnorm: Perform a Partition of Variance of Reaction Norms

rn_gen_decomp

R Documentation

Compute the decomposition of the additive genetic variance and their `\gamma`- and `\iota`-decomposition

Description

This function calculates the total additive genetic variance of the reaction norm (V_{\text{Add}}, and its \gamma-decomposition), the marginal additive genetic variance of the trait (V_{\text{A}}) and the additive genetic variance of plasticity (V_{\text{A}\times\text{E}}, and its \iota-decomposition).

Usage

rn_gen_decomp(theta, G_theta, env = NULL, shape = NULL, X = NULL, fixed = NULL,
              wt_env = NULL, compute_gamma = TRUE, compute_iota  = TRUE,
              add_vars = NULL, 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)
`compute_gamma`	Should the `\gamma`-decomposition be performed? Default is TRUE. (boolean)
`compute_iota`	Should the `\iota`-decomposition be performed? Default is TRUE. (boolean)
`add_vars`	Optional, provide additive genetic variances `V_{\text{Add}}`, `V_{\text{A}}` and `V_{\text{A}\times\text{E}}` (in that exact order!) computed from another model, e.g. a character-state model. These values will be used to scale the `\gamma`'s and `\iota`'s and be returned by the function for the respective additive genetic variances. (numeric vector of length 3)
`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{Add}} is the total additive genetic variance in the reaction norm. It can be decomposed according to each of the parameters in G_theta (and their pairwise covariance), using the \gamma-decomposition, if the compute_gamma is activated. It can also be decomposed into the marginal additive genetic variance of the trait (V_{\text{A}}, the additive genetic variance of the trait that would be computed if plasticity were ignored), and the additive genetic variance of plasticity itself (V_{\text{A}\times\text{E}}, i.e. the genetic-by-environment interaction variance). This last component can also be decomposed according to each of the parameters in G_theta (and their pairwise covariance), using the \iota-decomposition (for interaction).

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 values for V_{\text{Add}}, V_{\text{A}} and V_{\text{A}\times\text{E}}, as well as the \gamma- and \iota-decomposition if requested, formatted as a 1-row data.frame (data.frame, all numeric).

Author(s)

Pierre de Villemereuil

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
out <- 
  rn_gen_decomp(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

# Checking that V_Add = V_A + V_AxE
out$V_Add == out$V_A + out$V_AxE
# Checking that the sum of \eqn{\gamma}'s is 1
out$Gamma_cmax + out$Gamma_xopt + out$Gamma_cmax_xopt
# Checking that the sum of \eqn{\iota}'s is 1
out$Iota_cmax + out$Iota_xopt + out$Iota_cmax_xopt

# Applying some weighting to the environmental values according to a normal distribution
rn_gen_decomp(theta   = theta,
              G_theta = G,
              env     = vec_env,
              shape   = expr,
              fixed   = c(3, 4),
              wt_env  = dnorm(vec_env))
              
# 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_gen_decomp(theta   = theta,
              G_theta = G,
              X        = X)

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