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Sensitivity_Sim2.1_6parameters_parallel.R
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Sensitivity_Sim2.1_6parameters_parallel.R
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# ======================================================================================== #
# Sensitivity analysis of the model using variance based techniques for >>> 6 parameters <<< #
# description: Perform a sensitivity analysis for Simulation Sim2.1
# (single pesticide event with symmetric migration)
# - use a variance based Method described in Satelli 2010
# called soboljansen() in the package "sensitivity"
# - vary 6 main parameters, excluding the structural ones (l_eggs & l_adult)
# Author: Bernhard Kuehn
# last change: 20.02.2017
# revised by RBS (05.03.2017)
# ==================================================================================================== #
rm(list=ls(all=TRUE))
# set library
#.libPaths("/home/rstudio/R/x86_64-pc-linux-gnu-library/3.0")
# install.packages
# install.packages("sensitivity")
# install.packages("boot")
# install.packages("doParallel")
# install.packages("foreach")
# load libraries
library(sensitivity)
library(boot)
library(doParallel)
library(foreach)
#### short Model description #####
# Simulation 2.1: symmetic Migration, single exposure
# Pesticide event: single, on day pesticide (120)
# with symmetric migration from an upstream patch
# Affected parameters: prey population size Ni, emergence rate, growth rate in
# the larval phase. Reduction by 0, 25, 50, 75%, all
# combinations possible.
# Emigration rate: larvae 0.2, adult 0.3
# mortality rate of migration: 0.3 for larvae and 0.3 for adults
# set up cluster for parellel computing
# num_cores <- detectCores()-1
# cl <- makeCluster(num_cores)
# registerDoParallel(cl)
# --------------------------------------------------------------------------------- #
### Parameters ###
params = data.frame(# no theta logistic growth
eps_linst = 0.2, # migration rate larvae
eps_adult = 0.3, # migration rate adult
d_linst = 0.7, # 1-mortality larvae
d_adult = 0.7, # 1-mortality adult
s = 2, # migration shape parameter
day_pest = 120) # day of pesticide application
# ----------------------------------------------------------------------------------- #
# write the model in a different form (as function), so it is possible to use the function soboljansen() on it
simulate.model.sim2.1 = function(X){
stopifnot(require(simecol))
inits = data.frame(ini_Ni = 3000, # initial value patch A
ini_Nj = 3000, # initial value patch B
sim_years = 10 ) #number of simulated years
# constant parameter:
K = 3000 #
rd_linst = -log(1/2)/149 # exponential decay of larvae (150days)
l_egg = 40 # duration of egg growth in winter
l_adult = 40 # duration of adult period
# define growth-rate of eggs based on days eggs need to grow
r_earlinst <- -(log((1/0.9-1)*(0.5*K)/(K-(0.5*K)))/(l_egg))
# Recovery threshold
N_recov <- K * 0.9
# years
sim_years <- inits$sim_years # simulation years
#define years
i = seq(0,360*sim_years,by = 360)+1 # each start day of the year (e.g. 1, 361 ...)
# Reduction of parameters due to pesticide event
f_mort <- c(1, 0.75,0.5, 0.25) # reduces population size of prey (Ni)
f_emerg <- c(1, 0.75,0.5, 0.25) # reduces emergence rate
f_fecundity <- c(1, 0.75,0.5, 0.25) # reduces growth rate (r_earlinst)
N_E_G <- as.matrix(expand.grid(f_mort, f_emerg, f_fecundity))
# for sensitivity analysis:
# calculate model for a matrix input
# ........................................ #
# for parallelisation: nested foreach- loops
# ....................................... #
rec_times.all = foreach(iter = 1:nrow(X), .packages='simecol',.combine = 'rbind') %:%
# simulate one single exposure scenario with one predefined parameterset
foreach(z = 1:nrow(N_E_G),.combine = 'c') %dopar% {
#Matrix for population sizes at the beginning of the year
N_year <- matrix(NA, nrow=sim_years+1, ncol=2, dimnames = list(c(1:(sim_years+1)),c("Ni", "Nj")))
N_year[1,] <- c(inits$ini_Ni,inits$ini_Nj)
#Matrix for the daily population sizes, i.a. for plotting
N_daily <- matrix(NA, nrow=sim_years*360, ncol=3)
N_daily[1,] <- c(as.integer(1), inits$ini_Ni,inits$ini_Nj)
N_daily[,1] <- 1:(sim_years*360)
# ---------------------------------------------------- #
# Single exposure in the first year of the simulation:
# ---------------------------------------------------- #
# Day 1 - x exponential decrease of aquatic larvae due to predation
linst1_x <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = rd_linst, K = K,d = X[[iter,3]], eps = X[[iter,1]],
r2 = 0, s = X[[iter,5]]),
times = c(from = 1, to = X[[iter,6]], by = 1),
init = c(Ni = N_year[1,1],Nj = N_year[1,2]),
solver = "lsoda"
)
# Call ODE model
res_linst1_x <- sim(linst1_x)
# Store results as matrix
res_linst1_x_mat <- as.matrix(out(res_linst1_x))
# Day x - 150 Pesticide exposure & exponential decrease of aquatic larvae due to predation
linstx_150 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = rd_linst, K = K,d = X[[iter,3]], eps = X[[iter,1]],
r2 = 0, s = X[[iter,5]]),
times = c(from = X[[iter,6]], to = 150, by = 1),
# Pesticide exposure (f_mort), only Patch A effected
init = c(Ni = N_E_G[[z,1]]*as.vector(res_linst1_x_mat[nrow(res_linst1_x_mat),2]),
Nj = as.vector(res_linst1_x_mat[nrow(res_linst1_x_mat),3])),
solver = "lsoda"
)
# Call ODE model
res_linstx_150 <- sim(linstx_150)
# Store results as matrix
res_linstx_150_mat <-as.matrix(out(res_linstx_150))
# Day 151-190 Adults emerge
adult151_190 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = X[[iter,4]], eps = X[[iter,2]],
r2 = 0, s = X[[iter,5]], theta= X[[iter,1]]),
times = c(from = 151, to = 150+l_adult, by = 1),
# adult reduced by f_emerg, only Patch A effected
init = c(Ni = N_E_G[[z,2]] * as.vector(res_linstx_150_mat[nrow(res_linstx_150_mat),2]),
Nj = as.vector(res_linstx_150_mat[nrow(res_linstx_150_mat),3])),
solver = "lsoda"
)
# Call ODE model
res_adult151_190 <- sim(adult151_190)
# Store results as matrix
res_adult151_190_mat <-as.matrix(res_adult151_190@out)
# Day 191-360 Egg laying, growing of the population till carrying capacity is reached
earlinst191_360 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
# Pesticide event - reduction in r2: G * r2
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B (no pesticide)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = X[[iter,3]], eps = 0,
r2 = N_E_G[[z,3]]* r_earlinst, s = X[[iter,5]]),
times = c(from = 150+l_adult, to = 360, by = 1),
init = c(Ni = as.vector(res_adult151_190_mat[nrow(res_adult151_190_mat),2]),
Nj = as.vector(res_adult151_190_mat[nrow(res_adult151_190_mat),3])),
solver = "lsoda"
)
# Call ODE model
res_earlinst191_360 <- sim(earlinst191_360)
# Store results as matrix
res_earlinst191_360_mat <- as.matrix(res_earlinst191_360@out)
# store results of the whole year in N_daily-matrix for plotting
N_daily[i[1]:(i-1)[2],2:3] <- rbind(res_linst1_x_mat[,-1],
res_linstx_150_mat[-1,-1],
res_adult151_190_mat[,-1],
res_earlinst191_360_mat[-1,-1])
#Storing population size in N for following year
N_year[2,1] <- res_earlinst191_360_mat[nrow(res_earlinst191_360_mat),2]
N_year[2,2] <- res_earlinst191_360_mat[nrow(res_earlinst191_360_mat),3]
# --------------------------------------------------- #
# Rest of the simulation period: no further exposure
# --------------------------------------------------- #
for(j in 2:sim_years) {
# Day 1-150 exponential decrease of aquatic larvae due to predation
linst1_150 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = rd_linst, K = K,d = X[[iter,3]], eps = X[[iter,1]],
r2 = 0, s = X[[iter,5]]),
times = c(from = 1, to = 150, by = 1),
init = c(Ni = N_year[j,1],Nj = N_year[j,2]),
solver = "lsoda"
)
# Call ODE model
res_linst1_150 <- sim(linst1_150)
# Store results as matrix
res_linst1_150_mat <-as.matrix(out(res_linst1_150))
# Day 151-190 Adults emerge
adult151_190 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = X[[iter,4]], eps = X[[iter,2]],
r2 = 0, s = X[[iter,5]]),
times = c(from = 151, to = 150+l_adult, by = 1),
init = c(Ni = as.vector(res_linst1_150_mat[nrow(res_linst1_150_mat),2]),
Nj = as.vector(res_linst1_150_mat[nrow(res_linst1_150_mat),3])),
solver = "lsoda"
)
# Call ODE model
res_adult151_190 <- sim(adult151_190)
# Store results as matrix
res_adult151_190_mat <-as.matrix(res_adult151_190@out)
# Day 191-360 Egg laying, growing of the population till carrying capacity is reached
earlinst191_360 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch A
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K)) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch B
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K)) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = X[[iter,3]], eps = 0,
r2 = r_earlinst, s = X[[iter,5]]),
times = c(from = 150+l_adult, to = 360, by = 1),
init = c(Ni = as.vector(res_adult151_190_mat[nrow(res_adult151_190_mat),2]),
Nj = as.vector(res_adult151_190_mat[nrow(res_adult151_190_mat),3])),
solver = "lsoda"
)
# Call ODE model
res_earlinst191_360 <- sim(earlinst191_360)
# Store results as matrix
res_earlinst191_360_mat <-as.matrix(res_earlinst191_360@out)
# store results of the whole year in N_daily-matrix for plotting
N_daily[i[j]:(i-1)[j+1],2:3] <- rbind(res_linst1_150_mat[,-1],
res_adult151_190_mat[,-1],
res_earlinst191_360_mat[-1,-1])
#Storing population size in N for following year
N_year[j+1,1] <- res_earlinst191_360_mat[nrow(res_earlinst191_360_mat),2]
N_year[j+1,2] <- res_earlinst191_360_mat[nrow(res_earlinst191_360_mat),3]
} # end of time loop
### Calculate recovery times
# first value below threshold of K * 0.9
v1 <- which(N_daily[,2] < N_recov)[1]
# time until the threshold is reached again = recovery time
rec_time <- which(N_daily[(v1+1):nrow(N_daily),2] >= N_recov)[1]
rec_time
}
return(rec_times.all)
}
# # check how long single model evaluation takes
# ptm <- proc.time()
# simulate.model.sim2.1(rbind(params, params+params*0.1))
# proc.time() - ptm
#
# # Shutdown cluster neatly
# if(!is.null(cl)) {
# stopCluster(cl)
# stopImplicitCluster()
# cl <- c()
# }
# ====================================== #
# actual sensitivity analysis:
# variance based technique from sobol & jansen
# ====================================== #
# --------------------------------------- #
# prepare input for sensitivity analysis
# --------------------------------------- #
n <- 1000 # number of bootstrap samples
# which parameters are getting varied?
# theta, eps_linst, eps_adult, d_linst, d_adult, s, day_pest
# +-50%
# parameters constant: K, rd_linst.
# extra conditions for: day_pest upper limit = 150,
# d_linst ~ [0.5,1],
# d_adult ~ [0.5,1],
# no theta
# set upper limit
upper_limit = params + params*0.5
upper_limit$day_pest = 150
upper_limit$d_linst = 1
upper_limit$d_adult = 1
# set lower limit
lower_limit = params - params*0.5
lower_limit$day_pest = 90
lower_limit$d_linst = 0.5
lower_limit$d_adult = 0.5
# set initial values from an uniform distribution
X1 = X2 = matrix(ncol = length(params), nrow = n)
for(i in 1:length(params)) {
X1[,i] = runif(n,min = lower_limit[[i]],max = upper_limit[[i]])
X2[,i] <- runif(n,min = lower_limit[[i]],max = upper_limit[[i]])
}
# round values, where discrete input is required: (discrete timesteps in the model)
X1[,6] = floor(X1[,6])
X2[,6] = floor(X2[,6])
# define colnames for input data, otherwise sobol-function throws an error
colnames(X1) = colnames(X2) = colnames(params)
# --------------------------------------- #
# perform the sensitivity analysis
# and record the time the analysis takes
# --------------------------------------- #
# # ------------------- #
# # added on 10.02.2017
# # parellelisation
# # ------------------- #
#
# set up cluster for parellel computing
num_cores = detectCores()-2
cl<-makeCluster(num_cores)
registerDoParallel(cl)
# simulate and write execution time into console
ptm <- proc.time()
sens.out.S2.1.noStructuralChanges = tryCatch(
soboljansen(model = simulate.model.sim2.1,X1,X2,nboot = 1000),
error = function(e) print(e)
)
proc.time() - ptm
# save output
save(sens.out.S2.1.noStructuralChanges,file = "../Sens.out.S2.1.noStructuralChanges.RData")
# Shutdown cluster neatly
if(!is.null(cl)) {
stopCluster(cl)
stopImplicitCluster()
cl <- c()
}