R/heating_pulse2.R

In epcc: Simulating Populations of Ectotherms under Global Warming

#'Heating pulse-2
#'
#' @description This function allows simulating the effect of an environmental warming pulse on
#'              the abundance of ectotherm populations. After the pulse, the temperature stabilizes
#'              at a temperature q units greater than the initial value (temp_ini).
#'
#'
#'
#'@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 optimum temperature.
#'@param lambda Marginal loss by non-thermodependent intraspecific competition.
#'@param temp_peak Peak pulse temperature.
#'@param time_peak Time when temp_peak is reached.
#'@param q  Difference between initial and stabilization temperature.
#'@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 a rational function in which
#'         the temperature stabilizes at a different value after the pulse (that is,
#'         the final temperature differs from the initial temperature by q units).
#'         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.
#'#######################################################################
#'
#'heating_pulse2(y_ini = c(N = 100, N = 200, N = 400),
#'                temp_ini = rep(20,3),
#'                temp_cmin = rep(18,3),
#'                temp_cmax = rep(30,3),
#'                ro = rep(0.7,3),
#'                lambda = rep(0.00005,3),
#'                temp_peak = rep(29,3),
#'                time_peak = rep(2060,3),
#'                q = rep(3,3),
#'                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
#'
#'
#'heating_pulse2(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),
#'               temp_peak = rep(35,3),
#'               time_peak = rep(2060,3),
#'               q = rep(1,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'\donttest{
#'#######################################################################
#'   #Example 3: Different relationships between initial environmental
#'   #           temperature and optimum temperature.
#'#######################################################################
#'
#'temp_cmin <- 18
#'temp_cmax <- 30
#'
#'# 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
#'
#'heating_pulse2(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),
#'               temp_peak = rep(29,3),
#'               time_peak = rep(2060,3),
#'               q = rep(1,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'
#'#######################################################################
#'   #Example 4: Different peaks of temperature.
#'#######################################################################
#'
#'temp_peak3 <- 30
#'temp_peak2 <- 9/10*temp_peak3
#'temp_peak1 <- 9/10*temp_peak2
#'
#'heating_pulse2(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_ini = rep(19,3),
#'               temp_cmin = rep(18,3),
#'               temp_cmax = rep(30,3),
#'               ro = rep(0.7,3),
#'               lambda = rep(0.00005,3),
#'               temp_peak = c(temp_peak1,temp_peak2,temp_peak3),
#'               time_peak = rep(2060,3),
#'               q = rep(1,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'
#'#######################################################################
#'   #Example 5: Different marginal losses by a non-thermodependent
#'   #           component of intraspecific competition.
#'#######################################################################
#'
#'lambda3 <- 0.01
#'lambda2 <- 1/2*lambda3
#'lambda1 <- 1/2*lambda2
#'
#'heating_pulse2(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_ini = rep(26,3),
#'               temp_cmin = rep(18,3),
#'               temp_cmax = rep(30,3) ,
#'               ro = rep(0.7,3),
#'               lambda = c(lambda1,lambda2,lambda3),
#'               temp_peak = rep(29,3),
#'               time_peak = rep(2075,3),
#'               q = rep(1,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'}
###################################################


  heating_pulse2 <- function(y_ini = c(N = 400, N = 400, N = 400),
                             temp_ini = rep(20,3),
                             temp_cmin = rep(18,3),
                             temp_cmax = c(25,28,32),
                             ro = rep(0.7,3),
                             lambda = rep(0.00005,3),
                             temp_peak = rep(25,3),
                             time_peak = rep(2060,3),
                             q = rep(5,3),
                             time_start = 2005,
                             time_end = 2100,
                             leap = 1/12){

    times<- seq(time_start, time_end, leap)

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]){

if(temp_peak[1]>=(temp_ini[1]+q[1]) && temp_peak[2]>=(temp_ini[2]+q[2]) && temp_peak[3]>=(temp_ini[3]+q[3])){
if(time_start<=time_peak[1] && time_peak[1]<=time_end && time_start<=time_peak[2] &&
   time_peak[2]<=time_end  && time_start<=time_peak[3] && time_peak[3]<=time_end){



##########################################################
  # Temperature parameters
##########################################################

b1<- 2*(time_peak[1]-time_start)*(1-q[1]/(temp_peak[1]-temp_ini[1]))
a1<- (b1*(time_peak[1]-time_start))/2

b2<- 2*(time_peak[2]-time_start)*(1-q[2]/(temp_peak[2]-temp_ini[2]))
a2<- (b2*(time_peak[2]-time_start))/2

b3<- 2*(time_peak[3]-time_start)*(1-q[3]/(temp_peak[3] -temp_ini[3]))
a3<- (b3*(time_peak[3]-time_start))/2
##########################################################

P2C <- function (times,temp_ini,a,b,q) {
  T <-(q*(times-time_start)^{2})/((times-time_start)^{2}-b*(times-time_start)+a)+temp_ini

}


##########################################################
# 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)


##########################################################
# Time
##########################################################
time_op11=suppressWarnings((b1*(temp_op1-temp_ini[1])-sqrt(b1^2*(temp_op1-temp_ini[1])^2-
4*a1*(temp_op1-temp_ini[1])*(temp_op1-temp_ini[1]-q[1])))/(2*(temp_op1-temp_ini[1]-q[1]))+time_start)
time_op12=suppressWarnings((b1*(temp_op1-temp_ini[1])+sqrt(b1^2*(temp_op1-temp_ini[1])^2-
4*a1*(temp_op1-temp_ini[1])*(temp_op1-temp_ini[1]-q[1])))/(2*(temp_op1-temp_ini[1]-q[1]))+time_start)
time_cmax11=suppressWarnings((b1*(temp_cmax[1]-temp_ini[1])-sqrt(b1^2*(temp_cmax[1]-temp_ini[1])^2-
4*a1*(temp_cmax[1]-temp_ini[1])*(temp_cmax[1]-temp_ini[1]-q[1])))/(2*(temp_cmax[1]-temp_ini[1]-q[1]))+time_start)
time_cmax12=suppressWarnings((b1*(temp_cmax[1]-temp_ini[1])+sqrt(b1^2*(temp_cmax[1]-temp_ini[1])^2-
4*a1*(temp_cmax[1]-temp_ini[1])*(temp_cmax[1]-temp_ini[1]-q[1])))/(2*(temp_cmax[1]-temp_ini[1]-q[1]))+time_start)

  ##########################################################

time_op21=suppressWarnings((b2*(temp_op2-temp_ini[2])-sqrt(b2^2*(temp_op2-temp_ini[2])^2-
4*a2*(temp_op2-temp_ini[2])*(temp_op2-temp_ini[2]-q[2])))/(2*(temp_op2-temp_ini[2]-q[2]))+time_start)
time_op22= suppressWarnings((b2*(temp_op2-temp_ini[2])+sqrt(b2^2*(temp_op2-temp_ini[2])^2-
4*a2*(temp_op2-temp_ini[2])*(temp_op2-temp_ini[2]-q[2])))/(2*(temp_op2-temp_ini[2]-q[2]))+time_start)
time_cmax21= suppressWarnings((b2*(temp_cmax[2]-temp_ini[2])-sqrt(b2^2*(temp_cmax[2]-temp_ini[2])^2-
4*a2*(temp_cmax[2]-temp_ini[2])*(temp_cmax[2]-temp_ini[2]-q[2])))/(2*(temp_cmax[2]-temp_ini[2]-q[2]))+time_start)
time_cmax22= suppressWarnings((b2*(temp_cmax[2]-temp_ini[2])+sqrt(b2^2*(temp_cmax[2]-temp_ini[2])^2-
4*a2*(temp_cmax[2]-temp_ini[2])*(temp_cmax[2]-temp_ini[2]-q[2])))/(2*(temp_cmax[2]-temp_ini[2]-q[2]))+time_start)

  ##########################################################

time_op31=suppressWarnings((b3*(temp_op3-temp_ini[3])-sqrt(b3^2*(temp_op3-temp_ini[3])^2-
4*a3*(temp_op3-temp_ini[3])*(temp_op3-temp_ini[3]-q[3])))/(2*(temp_op3-temp_ini[3]-q[3]))+time_start)
time_op32= suppressWarnings((b3*(temp_op3-temp_ini[3])+sqrt(b3^2*(temp_op3-temp_ini[3])^2-
4*a3*(temp_op3-temp_ini[3])*(temp_op3-temp_ini[3]-q[3])))/(2*(temp_op3-temp_ini[3]-q[3]))+time_start)
time_cmax31= suppressWarnings((b3*(temp_cmax[3]-temp_ini[3])-sqrt(b3^2*(temp_cmax[3]-temp_ini[3])^2-
4*a3*(temp_cmax[3]-temp_ini[3])*(temp_cmax[3]-temp_ini[3]-q[3])))/(2*(temp_cmax[3]-temp_ini[3]-q[3]))+time_start)
time_cmax32= suppressWarnings((b3*(temp_cmax[3]-temp_ini[3])+sqrt(b3^2*(temp_cmax[3]-temp_ini[3])^2-
4*a3*(temp_cmax[3]-temp_ini[3])*(temp_cmax[3]-temp_ini[3]-q[3])))/(2*(temp_cmax[3]-temp_ini[3]-q[3]))+time_start)

#########################################################
##########################################################
  # Time limits
##########################################################
tM<-c(time_cmax11,time_cmax12,time_cmax21,time_cmax22,time_cmax31,
      time_cmax32)
tM_new <- tM
tM_new[is.nan(tM_new)] <- times[length(times)]

  if(times[length(times)]<tM_new[1]){
    tM_new[1]=times[length(times)]
  }
  if(times[length(times)]<tM_new[2]){
    tM_new[2]=times[length(times)]
  }
  if(times[length(times)]<tM_new[3]){
    tM_new[3]=times[length(times)]
  }

  if(times[length(times)]<tM_new[4]){
    tM_new[4]=times[length(times)]
  }

  if(times[length(times)]<tM_new[5]){
    tM_new[5]=times[length(times)]
  }

  if(times[length(times)]<tM_new[6]){
    tM_new[6]=times[length(times)]
  }

  if(tM_new[1]<=tM_new[2]){

    tM_new1<-tM_new[1]
  }else{
    tM_new1<-tM_new[2]
  }


  if(tM_new[3]<=tM_new[4]){

    tM_new2<-tM_new[3]
  }else{
    tM_new2<-tM_new[4]
  }

  if(tM_new[5]<=tM_new[6]){

    tM_new3<-tM_new[5]
  }else{
    tM_new3<-tM_new[6]
  }

##########################################################
  # Parameters
 ##########################################################
parms1<-c(temp_cmin[1],temp_ini[1],temp_cmax[1],temp_op1,ro[1],lambda[1])
parms2<-c(temp_cmin[2],temp_ini[2],temp_cmax[2],temp_op2,ro[2],lambda[2])
parms3<-c(temp_cmin[3],temp_ini[3],temp_cmax[3],temp_op3,ro[3],lambda[3])
##########################################################
    # Model for each trend
##########################################################
model1 <- function (times, y,parms1) {
      with(as.list(c(y)), {
 T <- P2C(times,temp_ini[1],a1,b1,q[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 <- P2C(times,temp_ini[2],a2,b2,q[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 <- P2C(times,temp_ini[3],a3,b3,q[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")
###############################################################
    # 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<tM_new1),aes(x=.data$x,
                               ymax=.data$y),ymin=0,alpha=0.3, fill="brown") +
geom_ribbon(data=subset(dat2,times>times[1] & times<tM_new2),aes(x=.data$x,
                              ymax=.data$y),ymin=0,alpha=0.3, fill="green4") +
geom_ribbon(data=subset(dat3,times>times[1] & times<tM_new3),aes(x=.data$x,
                                ymax=.data$y),ymin=0,alpha=0.3, fill="blue") +
geom_vline(xintercept = tM_new1, size=.5, color="brown",linetype="dashed")+
geom_vline(xintercept = tM_new2, size=.5, color="green4",linetype="dashed")+
geom_vline(xintercept = tM_new3, size=.5, color="blue",linetype="dashed")+
geom_line(data =subset(data1,times>times[1] & times<tM_new1), color = "brown")+
geom_line(data =subset(data2,times>times[1] & times<tM_new2), color = "green4")+
geom_line(data =subset(data3,times>times[1] & times<tM_new3), 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 = tM_new1, size=.5, color="brown",linetype="dashed")+
geom_vline(xintercept = tM_new2, size=.5, color="green4",linetype="dashed")+
geom_vline(xintercept = tM_new3, size=.5, color="blue",linetype="dashed")+
geom_line(data =subset(da1,times>times[1] & times<tM_new1), color = "brown")+
geom_line(data =subset(da2,times>times[1] & times<tM_new2), color = "green4")+
geom_line(data =subset(da3,times>times[1] & times<tM_new3), 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("It is recommended that the time in which the peak temperature is reached is within the time sequence")
          }

        }else{
stop("The peak temperature must be greater than or equal to the temp_ini+q")
        }

      }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")
    }


  }