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#' Periodic increasing temperature trend
#'
#' @description This function allows simulating the effect of increasing temperature
#' with periodic variability on the abundance of ectotherm populations.
#'
#'
#'
#'@param y_ini Initial population values (must be written with its name: N).
#'@param temp_ini Initial temperature.
#'@param temp_cmin Minimum critical temperature.
#'@param temp_cmax Maximum critical temperature.
#'@param ro Population growth rate at optimal temperature.
#'@param lambda Marginal loss by non-thermodependent intraspecific competition.
#'@param A Temperature wave amplitude.
#'@param B Parameter affecting the period of the trend (period is (2 pi)/|B|).
#'@param m Temperature increase slope.
#'@param time_start Start of time sequence.
#'@param time_end End of time sequence.
#'@param leap Time sequence step.
#'
#'@details Three populations and/or scenarios can be simulated simultaneously.
#' The temperature trend is determined by an expression that shows a linear
#' increment with periodic variability. The amplitude, period, and downward
#' speed of change can be specified. In each input vector, the parameters for
#' the three simulations must be specified (finite numbers for the initial
#' population abundance). The simulations are obtained by a model that incorporates
#' the effects of temperature over time, which leads to a non-autonomous ODE approach.
#' This is function uses the ODE solver implemented in the package deSolve
#' (Soetaert et al., 2010).
#'
#'
#'@return (1) A data.frame with columns having the simulated trends.
#'@return (2) A two-panel figure in which (a) shows the population abundance curves represented by
#' solid lines and the corresponding carrying capacities are represented by shaded areas.
#' In (b) the temperature trend is shown. The three simultaneous simulations are depicted
#' by different colors, i.e. 1st brown, 2nd green and 3rd blue.
#'
#'
#'@references Soetaert, K., Petzoldt, T., & Setzer, R. (2010). Solving Differential Equations in R: Package
#' deSolve. Journal of Statistical Software, 33(9), 1 - 25.
#' doi:http://dx.doi.org/10.18637/jss.v033.i09
#'
#'@export
#'@examples
#'
#'#######################################################################
#' #Example 1: Different initial population abundances.
#'#######################################################################
#'
#'increasing_periodicity(y_ini = c(N = 100, N = 200, N = 400),
#' temp_ini = rep(19,3),
#' temp_cmin = rep(18,3),
#' temp_cmax = rep(35,3),
#' ro = rep(0.7,3),
#' lambda = rep(0.00005,3),
#' A = rep(2,3),
#' B = rep(0.6,3),
#' m = rep(1/5,3),
#' time_start = 2005,
#' time_end = 2100,
#' leap = 1/12)
#'
#'#######################################################################
#' #Example 2: Different thermal tolerance ranges.
#'#######################################################################
#'
#'temp_cmin3 <- 18
#'temp_cmin2 <- 10/9*temp_cmin3
#'temp_cmin1 <- 10/9*temp_cmin2
#'
#'temp_cmax1 <- 32.4
#'temp_cmax2 <- 10/9*temp_cmax1
#'temp_cmax3 <- 10/9*temp_cmax2
#'
#'increasing_periodicity(y_ini = c(N = 100, N = 100, N = 100),
#' temp_ini = rep(23,3),
#' temp_cmin = c(temp_cmin1,temp_cmin2,temp_cmin3),
#' temp_cmax = c(temp_cmax1,temp_cmax2,temp_cmax3),
#' ro = rep(0.7,3),
#' lambda = rep(0.00005,3),
#' A = rep(2,3),
#' B = rep(0.6,3),
#' m = rep(1/5,3),
#' time_start = 2005,
#' time_end = 2300,
#' leap = 1/12)
#'\donttest{
#'#######################################################################
#' #Example 3: Different relationships between initial environmental
#' # temperature and optimum temperature.
#'#######################################################################
#'
#'temp_cmin <- 18
#'temp_cmax <- 40
#'
#'# Temperature at which performance is at its maximum value.
#'temp_op <- (temp_cmax+temp_cmin)/3+sqrt(((temp_cmax+temp_cmin)/3)^2-
#' (temp_cmax*temp_cmin)/3)
#'
#'temp_ini1 <- (temp_cmin+temp_op)/2
#'temp_ini2 <- temp_op
#'temp_ini3 <- (temp_op+temp_cmax)/2
#'
#'
#'increasing_periodicity(y_ini = c(N = 100, N = 100, N = 100),
#' temp_ini = c(temp_ini1,temp_ini2,temp_ini3),
#' temp_cmin = rep(temp_cmin,3),
#' temp_cmax = rep(temp_cmax,3),
#' ro = rep(0.7,3),
#' lambda = rep(0.00005,3),
#' A = rep(2,3),
#' B = rep(0.6,3),
#' m = rep(1/5,3),
#' time_start = 2005,
#' time_end = 2100,
#' leap = 1/12)
#'
#'#######################################################################
#' #Example 4: Different marginal losses by a non-thermodependent
#' # component of intraspecific competition.
#'#######################################################################
#'
#'lambda3 <- 0.01
#'lambda2 <- 1/2*lambda3
#'lambda1 <- 1/2*lambda2
#'
#'increasing_periodicity(y_ini = c(N = 100, N = 100, N = 100),
#' temp_ini = rep(19,3),
#' temp_cmin = rep(18,3),
#' temp_cmax = rep(35,3),
#' ro = rep(0.7,3),
#' lambda = c(lambda1,lambda2,lambda3),
#' A = rep(2,3),
#' B = rep(0.6,3),
#' m = rep(1/5,3),
#' time_start = 2005,
#' time_end = 2100,
#' leap = 1/12)
#'
#'#######################################################################
#' #Example 5: Different wave amplitude.
#'#######################################################################
#'
#'A3 <- 2
#'A2 <- 1/2 * A3
#'A1 <- 1/2 * A2
#'
#'increasing_periodicity(y_ini = c(N = 100, N = 100, N = 100),
#' temp_ini = rep(22,3),
#' temp_cmin = rep(18,3),
#' temp_cmax = rep(35,3),
#' ro = rep(0.7,3),
#' lambda = rep(0.00005,3),
#' A = c(A1,A2,A3),
#' B = rep(0.6,3),
#' m = rep(1/5,3),
#' time_start = 2005,
#' time_end = 2100,
#' leap = 1/12)
#'
#'#######################################################################
#' #Example 6: Different period.
#'#######################################################################
#'
#'B3 <- pi/5
#'B2 <- 1/2 * B3
#'B1 <- 1/2 * B2
#'
#'increasing_periodicity(y_ini = c(N = 100, N = 100, N = 100),
#' temp_ini = rep(22,3),
#' temp_cmin = rep(18,3),
#' temp_cmax = rep(35,3),
#' ro = rep(0.7,3),
#' lambda = rep(0.00005,3),
#' A = rep(2,3),
#' B = c(B1,B2,B3),
#' m = rep(1/5,3),
#' time_start = 2005,
#' time_end = 2100,
#' leap = 1/12)
#'}
###################################################
increasing_periodicity<- function(y_ini = c(N = 400, N = 400, N = 400),
temp_ini = rep(25,3),
temp_cmin = rep(18,3),
temp_cmax = c(25,28,32),
ro = rep(0.7,3),
lambda = rep(0.00005,3),
A = rep(5,3),
B = rep(0.06,3),
m = rep(1/5,3),
time_start = 2005,
time_end = 2300,
leap = 1/12){
times<- seq(time_start, time_end, leap)
PC <- function (times,temp_ini,temp_cmin,temp_cmax,m, A,B) {
T <- temp_ini+A*sin(B*(times-time_start))+ m*(times-time_start)
}
if(temp_cmin[1]<temp_cmax[1] && temp_cmin[2]<temp_cmax[2] && temp_cmin[3]<temp_cmax[3] ){
if(temp_cmin[1]<=temp_ini[1] && temp_ini[1]<=temp_cmax[1] && temp_cmin[2]<=temp_ini[2] &&
temp_ini[2]<=temp_cmax[2] && temp_cmin[3]<=temp_ini[3] && temp_ini[3]<=temp_cmax[3]){
##########################################################
# Optimum growing temperature
##########################################################
temp_op1<- ( temp_cmax[1]+temp_cmin[1])/3+sqrt((( temp_cmax[1]+
temp_cmin[1])/3)^2-( temp_cmax[1]*temp_cmin[1])/3)
temp_op2<- ( temp_cmax[2]+temp_cmin[2])/3+sqrt((( temp_cmax[2]+
temp_cmin[2])/3)^2-( temp_cmax[2]*temp_cmin[2])/3)
temp_op3<- ( temp_cmax[3]+temp_cmin[3])/3+sqrt((( temp_cmax[3]+
temp_cmin[3])/3)^2-( temp_cmax[3]*temp_cmin[3])/3)
##########################################################
# Parameters
##########################################################
parms1<-c(temp_cmin[1],temp_ini[1], temp_cmax[1],temp_op1,ro[1], lambda[1],m[1],A[1],B[1])
parms2<-c(temp_cmin[2],temp_ini[2], temp_cmax[2],temp_op2,ro[2], lambda[2],m[2],A[2],B[2])
parms3<-c(temp_cmin[3],temp_ini[3], temp_cmax[3],temp_op3,ro[3], lambda[3],m[3],A[3],B[3])
##########################################################
##########################################################
# Model for each trend
##########################################################
model1 <- function (times, y,parms1 ) {
with(as.list(c(y)), {
T <- PC(times,temp_ini[1],temp_cmin[1],temp_cmax[1],m[1],A[1],B[1])
r1<- rate_TPC(T,ro[1],temp_cmin[1], temp_cmax[1],temp_op1)
dN <- r1 * N * (1 - lambda[1]*(N / r1))
list(dN,T,r1) })
}
###############################################################
model2 <- function (times, y,parms2) {
with(as.list(c(y)), {
T <- PC(times,temp_ini[2],temp_cmin[2],temp_cmax[2],m[2],A[2],B[2])
r2<- rate_TPC(T,ro[2],temp_cmin[2], temp_cmax[2],temp_op2)
dN <- r2 * N * (1 - lambda[2]*(N / r2))
list(dN,T,r2)})
}
###############################################################
model3 <- function (times, y,parms3) {
with(as.list(c(y)), {
T <- PC(times,temp_ini[3],temp_cmin[3],temp_cmax[3],m[3],A[3],B[3])
r3<- rate_TPC(T,ro[3],temp_cmin[3], temp_cmax[3],temp_op3)
dN <- r3 * N * (1 - lambda[3]*(N / r3))
list(dN,T,r3)})
}
###############################################################
###############################################################
# Solution
##############################################################
out1 <- ode(y=y_ini[1], times, model1, parms1 ,method = "ode45")
out2 <- ode(y=y_ini[2], times, model2, parms2, method = "ode45")
out3 <- ode(y=y_ini[3], times, model3, parms3, method = "ode45")
###############################################################
###############################################################
# Time limits
###############################################################
times_new1<-vector(mode = "numeric", length = 0)
times_new2<-vector(mode = "numeric", length = 0)
times_new3<-vector(mode = "numeric", length = 0)
for (i in 2: length(times)){
if((out1[i-1,3]-temp_cmin[1])>=0 && (out1[i,3]-temp_cmin[1])<0){
times_new1[i-1]<- times[i-1]
}else if((out1[i-1,3]-temp_cmin[1])<=0 && (out1[i,3]-temp_cmin[1])>0){
times_new1[i-1]<- times[i-1]
}else{
times_new1[i-1]<- 0
}
}
for (i in 2: length(times)){
if((out2[i-1,3]-temp_cmin[2])>=0 && (out2[i,3]-temp_cmin[2])<0){
times_new2[i-1]<- times[i-1]
}else if((out2[i-1,3]-temp_cmin[2])<=0 && (out2[i,3]-temp_cmin[2])>0){
times_new2[i-1]<- times[i-1]
}else{
times_new2[i-1]<- 0
}
}
for (i in 2: length(times)){
if((out3[i-1,3]-temp_cmin[3])>=0 && (out3[i,3]-temp_cmin[3])<0){
times_new3[i-1]<- times[i-1]
}else if((out3[i-1,3]-temp_cmin[3])<=0 && (out3[i,3]-temp_cmin[3])>0){
times_new3[i-1]<- times[i-1]
}else{
times_new3[i-1]<- 0
}
}
index1<- which(times_new1!=0)[1]
index2<- which(times_new2!=0)[1]
index3<- which(times_new3!=0)[1]
index1<- as.integer(index1)
index2<- as.integer(index2)
index3<- as.integer(index3)
if(!is.na(as.integer(index1))==FALSE){
times_inf1<- times[length(times)]
}else{
times_inf1<- times[index1]
}
if(!is.na(as.integer(index2))== FALSE){
times_inf2<- times[length(times)]
}else{
times_inf2<- times[index2]
}
if(!is.na(as.integer(index3))== FALSE){
times_inf3<- times[length(times)]
}else{
times_inf3<- times[index3]
}
#############################################################
#############################################################
times_new4<-vector(mode = "numeric", length = 0)
times_new5<-vector(mode = "numeric", length = 0)
times_new6<-vector(mode = "numeric", length = 0)
for (i in 2: length(times)){
if(( temp_cmax[1]-out1[i-1,3])>=0 && ( temp_cmax[1]-out1[i,3])<0){
times_new4[i-1]<- times[i-1]
}else if(( temp_cmax[1]-out1[i-1,3])<=0 && ( temp_cmax[1]-out1[i,3])>0){
times_new4[i-1]<- times[i-1]
}else{
times_new4[i-1]<- 0
}
}
for (i in 2: length(times)){
if(( temp_cmax[2]-out2[i-1,3])>=0 && ( temp_cmax[2]-out2[i,3])<0){
times_new5[i-1]<- times[i-1]
}else if(( temp_cmax[2]-out2[i-1,3])<=0 && ( temp_cmax[2]-out2[i,3])>0){
times_new5[i-1]<- times[i-1]
}else{
times_new5[i-1]<- 0
}
}
for (i in 2: length(times)){
if(( temp_cmax[3]-out3[i-1,3])>=0 && ( temp_cmax[3]-out3[i,3])<0){
times_new6[i-1]<- times[i-1]
}else if(( temp_cmax[3]-out3[i-1,3])<=0 && ( temp_cmax[3]-out3[i,3])>0){
times_new6[i-1]<- times[i-1]
}else{
times_new6[i-1]<- 0
}
}
index4<- which(times_new4!=0)[1]
index5<- which(times_new5!=0)[1]
index6<- which(times_new6!=0)[1]
index4<- as.integer(index4)
index5<- as.integer(index5)
index6<- as.integer(index6)
if(!is.na(as.integer(index4))== FALSE){
times_sup1<- times[length(times)]
}else{
times_sup1<- times[index4]
}
if(!is.na(as.integer(index5))== FALSE){
times_sup2<- times[length(times)]
}else{
times_sup2<- times[index5]
}
if(!is.na(as.integer(index6))== FALSE){
times_sup3<- times[length(times)]
}else{
times_sup3<- times[index6]
}
#############################################################
#############################################################
if(times_inf1<= times_sup1){
times_ext1<-times_inf1
}else{
times_ext1<-times_sup1
}
if(times_inf2<=times_sup2){
times_ext2<-times_inf2
}else{
times_ext2<-times_sup2
}
if(times_inf3<=times_sup3){
times_ext3<-times_inf3
}else{
times_ext3<-times_sup3
}
###############################################################
# Temperature trend
##############################################################
da1<-data.frame('x'=times,'y'=out1[,3] )
da2<-data.frame('x'=times,'y'=out2[,3] )
da3<-data.frame('x'=times,'y'=out3[,3] )
###############################################################
# Abundance
##############################################################
data1<-data.frame('x'=times,'y'=out1[,2] )
data2<-data.frame('x'=times,'y'=out2[,2] )
data3<-data.frame('x'=times,'y'=out3[,2] )
###############################################################
# Carrying capacity
##############################################################
K1=out1[,4]/lambda[1]
K2=out2[,4]/lambda[2]
K3=out3[,4]/lambda[3]
dat1<-data.frame('x'=times,'y'=K1 )
dat2<-data.frame('x'=times,'y'=K2 )
dat3<-data.frame('x'=times,'y'=K3 )
###############################################################
# Data
###############################################################
Data<- data.frame(times,out1[,3],out1[,2],K1,out2[,3],out2[,2],
K2,out3[,3],out3[,2],K3)
names(Data)<- c("Time","Temperature Scenario 1","Abundance scenario 1",
"Carrying capacity scenario 1","Temperature scenario 2",
"Abundance scenario 2","Carrying capacity scenario 2",
"Temperature scenario 3","Abundance scenario 3","Carrying
capacity scenario 3")
u<- formattable(Data, align = c("l", rep("r", NCOL(Data))))
print(u)
###############################################################
# Plots
##############################################################
data<-rbind(data1,data2,data3,dat1,dat2,dat3,da1,da2,da3)
p1<- ggplot(data, aes(x=.data$x, y=.data$y)) +
theme_bw()+
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank())+
geom_ribbon(data=subset(dat1,times>times[1] & times<times_ext1),aes(x=.data$x,
ymax=.data$y),ymin=0,alpha=0.3, fill="brown") +
geom_ribbon(data=subset(dat2,times>times[1] & times<times_ext2),aes(x=.data$x,
ymax=.data$y),ymin=0,alpha=0.3, fill="green4") +
geom_ribbon(data=subset(dat3,times>times[1] & times<times_ext3),aes(x=.data$x,
ymax=.data$y),ymin=0,alpha=0.3, fill="blue") +
geom_vline(xintercept = times_ext1, size=.5, color="brown",linetype="dashed")+
geom_vline(xintercept = times_ext2, size=.5, color="green4",linetype="dashed")+
geom_vline(xintercept = times_ext3, size=.5, color="blue",linetype="dashed")+
geom_line(data =subset(data1,times>times[1] & times<times_ext1), color = "brown")+
geom_line(data =subset(data2,times>times[1] & times<times_ext2), color = "green4")+
geom_line(data =subset(data3,times>times[1] & times<times_ext3), color = "blue")+
labs(x = "Time",y="Abundance")+
theme(plot.title = element_text(size=40))+
theme(plot.title = element_text(hjust = 0.5))+
theme(axis.title.y = element_text(size = rel(1), angle = 90))+
theme(axis.title.x = element_text(size = rel(1), angle = 00))+
labs(tag = "(a)")
p2<- ggplot(data, aes(x=.data$x, y=.data$y)) +
theme_bw()+
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank())+
geom_vline(xintercept = times_ext1, size=.5, color="brown",linetype="dashed")+
geom_vline(xintercept = times_ext2, size=.5, color="green4",linetype="dashed")+
geom_vline(xintercept = times_ext3, size=.5, color="blue",linetype="dashed")+
geom_line(data =subset(da1,times>times[1] & times<times_ext1), color = "brown")+
geom_line(data =subset(da2,times>times[1] & times<times_ext2), color = "green4")+
geom_line(data =subset(da3,times>times[1] & times<times_ext3), color = "blue")+
labs(x = "Time",y="Temperature")+
theme(axis.title.y = element_text(size = rel(1), angle = 90))+
theme(axis.title.x = element_text(size = rel(1), angle = 00))+
labs(tag = "(b)")
plot_grid(p1, p2)
}else{
stop("The initial study temperature must be within the thermal tolerance range")
}
}else{
stop("The minimum critical temperature must be less than the maximum critical temperature")
}
}
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