Exemplary:

#' @title
#' Genetic Gain for a trait when selecting for Carcass fat.
#' @description
#' This function computes the genetic gain in trait unit / year of the selection on carcass fat.
#' @param genetic_var_cov   The genetic variance-covariance matrix between the involved traits in the aggregate genotype.
#' @param residual_var_cov  The genetic variance-covariance matrix between the involved traits in the aggregate genotype.
#' @param male_offspring    Number of the assumed offspring of the male selection candidate when selection occurs.
#' @param female_offspring    Number of the assumed offspring of the female selection candidate when selection occurs.
#' @param proportion_calves Proportion of calves in the offspring.
#' @param proportion_adults Proportion of adults in the offspring.
#' @param male_proportionselected Proportion selected of the offspring of a male selection candidate
#' @param female_proportionselected Proportion selected of the offspring of a female selection candidate
#' @param male_generationintervall Generation intervall of the male selection path.
#' @param female_generationintervall Generation intervall of the female selection path.
#' @param economic_weights A vector of economic weights with lenght of number of traits.
#' @param trait A character of the trait name, e.g. "CCa". The trait names must also be existing in the headers of the matrices.
#' @return                 Genetic Gain in trait unit per year
#' @export compute_genetic_gain_trait_CF
compute_genetic_gain_trait_CF <- function(genetic_var_cov,
                                          residual_var_cov,
                                          offspring,
                                          proportion_calves,
                                          proportion_adults,
                                          male_proportionselected,
                                          female_proportionselected,
                                          male_generationintervall,
                                          female_generationintervall,
                                          economic_weights,
                                          trait){
  # define vector of economic weights
  a <- economic_weights

  # Intesity of selection
  male_i <- dnorm(qnorm(1-male_proportionselected))/male_proportionselected
  female_i <- dnorm(qnorm(1-female_proportionselected))/female_proportionselected

  # Covariance matrices

  C <- compute_covariance_matrices(genetic_var_cov = genetic_var_cov, residual_var_cov = residual_var_cov, offspring = offspring, proportion_calves = proportion_calves, proportion_adults = proportion_adults)

  # Number of traits
  n <- as.numeric(ncol(C))

  # male
  male_C <- C[1:n,]
  # female
  female_C <- C[(1+n):(2*n),]

  # Asymptotic covariance matrices

  Ca <- compute_asymptotic_covariance_matrices(genetic_var_cov = genetic_var_cov, residual_var_cov = residual_var_cov, offspring = offspring, proportion_calves = proportion_calves, proportion_adults = proportion_adults,male_proportionselected = male_proportionselected,female_proportionselected = female_proportionselected)

  # Number of traits
  n <- as.numeric(ncol(Ca))

  # male
  male_Ca <- Ca[1:n,]
  # female
  female_Ca <- Ca[(1+n):(2*n),]

  # P matrix extraction from C
  male_P <- male_C[3:4,3:4]
  female_P <- female_C[3:4,3:4]

  # W matrix extraction from C
  male_W <- male_C[,3:4]
  female_W <- female_C[,3:4]

  # b computation
  male_b <- solve(male_P)%*%t(male_W)%*%a
  female_b <- solve(female_P)%*%t(female_W)%*%a

  # asymptotic P matrix extraction from asymptotic C
  male_Pa <- male_Ca[3:4,3:4]
  female_Pa <- female_Ca[3:4,3:4]

  # Genetic Gain
  Qtrait_CF<- (male_i/sqrt(t(male_b)%*%male_Pa%*%male_b)*t(male_b)%*%male_Ca[3:4,trait]+female_i/sqrt(t(female_b)%*%female_Pa%*%female_b)*t(female_b)%*%female_Ca[3:4,trait])/(male_generationintervall+female_generationintervall)

  Qtrait_CF <- as.numeric(Qtrait_CF)

  return(Qtrait_CF)
}