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Sim1_NoMigr_SingEx.R
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Sim1_NoMigr_SingEx.R
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# --------------------------------------------- #
# Simulation 1 for scenario:
# --------------------------------------------- #
# Pesticide event: single exposure, on day 120
# No migration from an upstream patch
library(simecol)
# needs ajdustment to your path:
setwd("~/Desktop/Modelling_Twopatch/Latest_scripts/results")
# --------------------------------------------------------------------------------- #
### Parameters ###
# Carrying capacity
K <- 3000 # following Speirs 2000
# Recovery threshold
N_recov <- K * 0.9
# Initial population sizes
N_i = N_j <- K
# parameter for theta-logistic growth
theta <- 1
# we only model logistic growth, but setting the parameter to different values
# allows to implement theta logistic growth, but see discussion in:
# Clark F., Brook B.W., Delean S., Reşit Akçakaya H. & Bradshaw C.J.A. (2010)
# The theta-logistic is unreliable for modelling most census data.
# Methods in Ecology and Evolution 1, 253–262.
# growth rates
m_linst <- -log(1/2)/149 # Mortality rate for water phase
l_earlinst <- 40
r_earlinst <- -(log((1/0.9^theta-1)*(0.5*K)^theta/(K^theta-(0.5*K)^theta))/(l_earlinst*theta))
# Immigration parameters
eps_linst <- eps_adult <- 0 # no migration in this scenario
d_linst <- 0.7 # 1-d <- migration mortality, i.e. 0.3 for late instar larvae and 0.3 for adults
d_adult <- 0.7
s <- 2 #
### Pesticide Parameters ###
day_pesticide <- 120 # day where the pesticide enters the water column
# Reduction of parameters due to pesticide event
f_mort <- c(1, 0.75,0.5, 0.25) # reduces population size of population (N_i)
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)
# ----------------------------------------------------------------------------------- #
# years
sim_years <- 10 # simulation years
i <- seq(0,360*sim_years,by = 360)+1 # each start day of the year (e.g. 1, 361 ...)
# 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(N_i,N_j)
# 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), N_i,N_j)
N_daily[,1] <- 1:(sim_years*360)
### Simulate first year with pesticide event and no migration
d <- NULL
for (N in f_mort){
for (E in f_emerg){
for (G in f_fecundity){
# ---------------------------------------------------- #
# Single exposure in the first year of the simulation:
# ---------------------------------------------------- #
# Day 1 to day_pesticide exponential decrease of aquatic late instars (see paper)
linst1_x <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch I (polluted)
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = m_linst, K = K, d = d_linst, eps = eps_linst,
r2 = 0, s = s, theta = theta),
times = c(from = 1, to = day_pesticide, by = 1),
init = c(Ni = N_year[1,1],Nj = N_year[1,2]),
solver = "lsoda"
)
# call model
res_linst1_x <- sim(linst1_x)
# Store results as matrix
res_linst1_x_mat <-as.matrix(out(res_linst1_x))
# Day day_pesticide to 150 Pesticide exposure & decrease of aquatic late instars
linstx_150 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch I (polluted)
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = m_linst, K = K,d = d_linst, eps = eps_linst,
r2 = 0, s = s, theta = theta, N = N),
times = c(from = day_pesticide, to = 150, by = 1),
# Pesticide exposure (f_mort), only Patch I (polluted) effected
init = c(Ni = N*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
adult_exp_151_190 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch I (polluted)
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = d_adult, eps = eps_adult,
r2 = 0, s = s, theta= theta),
times = c(from = 151, to = 190, by = 1),
# emergence reduced by f_emerg, only Patch I (polluted) effected
init = c(Ni = E * 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(adult_exp_151_190)
# Store results as matrix
res_adult151_190_mat <-as.matrix(res_adult151_190@out)
# Day 191-360 Oviposition and growing of the population
earlinst_exp_191_360 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch I (polluted)
# Pesticide event - reduction in r2: G * r2
dNi <- -r1 * Ni +
G * r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream) (no pesticide)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = d_linst, eps = 0,
r2 = r_earlinst, s = s, theta = theta),
times = c(from = 190, 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(earlinst_exp_191_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 to 150 exponential decrease of aquatic late instars (see paper)
linst1_150 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch I (polluted)
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = m_linst, K = K,d = d_linst, eps = eps_linst,
r2 = 0, s = s, theta = theta),
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- to 190 Adults emerge
adult151_190 <- new("odeModel",
main = function (time, init, parms) {
with(as.list(c(init, parms)), {
# Patch I (polluted)
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = d_adult, eps = eps_adult,
r2 = 0, s = s, theta= theta),
times = c(from = 151, to = 190, 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 I (polluted)
dNi <- -r1 * Ni +
r2 * Ni * (1 - (Ni / K) ^ theta) -
eps * (Ni / K) ^ s * Ni +
d * eps * (Nj / K) ^ s * Nj
# Patch J (upstream)
dNj <- -r1 * Nj +
r2 * Nj * (1 - (Nj / K) ^ theta) -
eps * (Nj / K) ^ s * Nj +
d * eps * (Ni / K) ^ s * Ni
list(c(dNi,dNj))
})
},
parms = c(r1 = 0, K = K,d = d_linst, eps = 0,
r2 = r_earlinst, s = s, theta = theta),
times = c(from = 190, 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
# store output
d <- rbind(d, cbind(as.data.frame(N_daily), N, E, G))
}
}
}
names(d) <- c("Day", "N_i", "N_j", "f_mort", "f_emerg", "f_fecundity")
d$treat <- as.factor(paste(d$f_mort,d$f_emerg, d$f_fecundity, sep="_"))
### compute minimum for Ni
v_min <- do.call("rbind", (as.list(by(d[,2], factor(d$treat), min))))
### Calculate recovery times
# first value below threshold of K * 0.9
v1 <- do.call("rbind", (as.list(by(d[,2], factor(d$treat), function(x) which(x < N_recov)[1]))))
# time until the threshold is reached again = recovery time
rec_time <- data.frame(matrix(data = NA, ncol=2, nrow=length(v1)))
names(rec_time) <- c("Rec_time", "treat")
temp_rec <- NULL
for(I in 1:length(levels(d$treat))) {
# extract data
temp_rec <- d[d$treat == levels(d$treat)[I],2]
rec_time[I,1] <- which(temp_rec[v1[I]:length(temp_rec)] >= N_recov)[1]
rec_time[I,2] <- levels(d$treat)[I]
}
# merge results
v2 <- data.frame(v1, row.names=NULL)
v2$treat <- rownames(v1)
v3 <- data.frame(v_min, row.names=NULL)
v3$treat <- rownames(v_min)
diff_temp_a <- merge(rec_time, v2)
diff_temp <- merge(diff_temp_a, v3)
# for comparison of different scenarios with different baseline recovery times
# calculation of difference to baseline scenario:
diff_temp$diff = abs(diff_temp[diff_temp$treat=="1_1_1", "Rec_time"] - diff_temp[ , "Rec_time"])
# add individual factors
fac1 <- unique(d[ ,4:6])
fac1$treat <- as.factor(paste(fac1$f_mort,fac1$f_emerg, fac1$f_fecundity, sep="_"))
final <- merge(diff_temp, fac1)
# calculation for upstream patch
# dir.create(paste0(getwd(),"/figures"))
# Plot Ni (Patch I (polluted)) and Nj
for(I in 1:length(levels(d$treat)))
{
png(filename = file.path(getwd(), paste0("figures/", "Sim1_SingleEvent_NoMigr", levels(d$treat)[I], ".png")))
plot(d[d$treat == levels(d$treat)[I],1], d[d$treat == levels(d$treat)[I],2], xlab = "Time [d]", ylab = "Population size",
type = "l", lty = 2, lwd = 2, ylim = c(0,7000))
lines(d[d$treat == levels(d$treat)[I],1], d[d$treat == levels(d$treat)[I],3], type = "l", lty = 1, lwd = 2)
legend(20,6980, c("Ni"),lty = 2, lwd=2)
legend(20,5900, c("Nj"), lty=1, lwd=2)
text(c(2200,2200,3200,3200,3200), c(6980,5900,6980,6480,5900), labels=c(
eps_linst,eps_adult, unique(d[d$treat == levels(d$treat)[I],"f_mort"]), unique(d[d$treat == levels(d$treat)[I],"f_emerg"]), unique(d[d$treat == levels(d$treat)[I],"f_fecundity"])), cex = 0.9)
text(c(1700,1700,2800,2800,2800), c(6980,5900,6980,6480,5900), c("eps_linst =",
"eps_adult =","f_mort =","f_emerg =","f_fecundity ="), cex = 0.9)
dev.off()
}
# Export daily population size
write.csv(final, file= paste0(getwd(),"/Sim1_NoMigr_SingEx_rec_time_new.csv"), row.names=F)
# Save recovery times
write.csv(d, file = paste0(getwd(),"/Z_Sim1_NoMigr_SingEx_daily_Ns.csv"))