Exemplary:

#' @title
#' Correlated genetic gain in trait unit / year for index.
#' @description
#' This function computes the correlated genetic gain in trait unit / year of the selection on the index. In this index all traits are represented in the aggregate genotype.
#' @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 The name of the trait, of which the genetic gain should be.
#' @return                 Correlated genetic gain in trait unit per year
#' @export compute_genetic_gain_trait
compute_genetic_gain_trait <- 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

  # 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),]

  # Correlated genetic gain
  Qtrait <- (male_i*as.numeric(t(a)%*%male_Ca[,trait])*1/(sqrt(as.numeric(t(a)%*%male_Ca%*%a))) +
               female_i*as.numeric(t(a)%*%female_Ca[,trait]) * 1/(sqrt(as.numeric(t(a)%*%female_Ca%*%a))))/(male_generationintervall+female_generationintervall)

  return(Qtrait)
}