R/metaco_sim_functions.R

In javirudolph/metaco2: Package associated to manuscript

#' @title Immigration Function
#' @export

I_f <- function(Y = "Species occurrence matrix",
                K = "Patch connectivity matrix",
                m = "outside immigration"){
  N <- nrow(Y)
  R <- ncol(Y)
  I <- (1-m) * (K %*% Y) / (K %*% matrix(1, nrow = N, ncol = R)) + m
  return(I)
}


#' @title Patch Connectivity
#' @export

get_K <- function(XY, alpha){
  N <- nrow(XY)
  distMat <- as.matrix(dist(XY, method = "euclidean", upper = T, diag = T))
  ConMat <- exp((-1/alpha)*distMat)
  diag(ConMat) <- 0
  return(ConMat)
}

#' @title Env Response - gaussian
#' @description The effect of the environment on the local performance and colonization
#' @export
#'
S_f_gaussian <- function(E, u_c, s_c) {
  R <- ncol(u_c)
  N <- nrow(E)
  D <- ncol(E)
  S <- matrix(1, nr = N, nc = R)
  for(i in 1:D){
    optima <- matrix(u_c[i,],nrow = N,ncol = R,byrow = TRUE)
    breadth <- matrix(s_c[i,],nrow = N,ncol = R,byrow = TRUE)^2
    S <- S*exp(-(E[,i]-optima)^2 / breadth)
  }
  return(S)
}

#' @title Env response quadratic
#' @description This function is used for a quadratic response to the environment
#' @export

S_f_quadratic <- function(E, u_c, s_c) {
  R <- ncol(u_c)
  N <- nrow(E)
  D <- ncol(E)
  S <- matrix(1, nr = N, nc = R)
  for(i in 1:D){
    optima <- matrix(u_c[i,],nrow = N,ncol = R,byrow = TRUE)
    breadth <- matrix(s_c[i,],nrow = N,ncol = R,byrow = TRUE)
    S <- S * ((-1 / (breadth/2)^2) * (E[,i] - optima)^2 + 1)
    S <- ifelse(S < 0, 0 , S)

  }
  return(S)
}


#' @title Interactions
#' @description  First get the sum of ecological interactions
#' @export
#'
sum_interactions <- function(A = "Species interactions matrix",
                             Y = "Species occurrence matrix"){
  t(A %*% t(Y))
}

#' @title The effect of interactions on colonization
#' @export
C_f <- function(v = "Sum interactions",
                d_c = "Sensitivity to interactions",
                c_0 = "Colonization at zero interactions",
                c_max = "Colonization at max interactions"){

  c_max * (1 + ((1 / c_0) - 1) * exp(-v * d_c))^-1
  # Is this the same as:
  # c_max / (1 + ((1 / c_0) - 1) * exp(-v * d_c))

}





#' @title Effect of environment over extinction
#' @export

M_f <- function(E = "Environmental variables",
                u_e = "extinction rate at optimum?",
                s_e = "extinction rate at optimum?") {
  R <- ncol(u_e)
  N <- nrow(E)
  D <- ncol(E)
  M <- matrix(1, nrow = N, ncol = R)
  for(i in 1:D){
    optima <- matrix(u_e[i,],nrow = N,ncol = R,byrow = TRUE)
    minima <- matrix(s_e[i,],nrow = N,ncol = R,byrow = TRUE)^2
    M <- M*(1 - exp(-(E[,i] - optima)^2 / minima))
  }
  return(M)
}


#' @title Effect of species interactions on extinction
#' @export

E_f <- function(v = "Sum of interactions",
                d_e = "Sensitivity to interactions",
                e_0 = "Extinction at zero interactions",
                e_min = "Extinction at max intreractions?") {
  N <- nrow(v)
  R <- ncol(v)

  e_min_mat <- matrix(e_min, nrow = N, ncol = R, byrow=TRUE)

  e_min_mat + (1 / (1-e_min_mat) + (1/(e_0-e_min_mat) - 1 / (1 - e_min_mat)) * exp(d_e * v))^-1

}