R/cooling_pulse1.R

In epcc: Simulating Populations of Ectotherms under Global Warming

#'Cooling pulse-1
#'
#' @description This function allows simulating the effect of an environmental
#'              cooling pulse on the abundance of ectotherm populations. After
#'              the pulse, the temperature stabilizes at a specific temperature
#'              (temp_a).
#'
#'@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 sd Vector of standard deviations associated with temperature trend.
#'@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 Gaussian function, whose
#'         main parameters are the mean and standard deviation. In each input
#'         vector, the parameters for the three simulations must be specified
#'         (finite numbers for 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.
#'#######################################################################
#'
#'cooling_pulse1(y_ini = c(N = 100, N = 200, N = 400),
#'               temp_ini = rep(26,3),
#'               temp_cmin = rep(18,3),
#'               temp_cmax = rep(30,3),
#'               ro = rep(0.7,3),
#'               lambda = rep(0.00005,3),
#'               temp_peak = rep(19,3),
#'               time_peak = rep(2060,3),
#'               sd = rep(10,3),
#'               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
#'
#'
#'cooling_pulse1(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_ini = rep(30,3),
#'               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(19,3),
#'               time_peak = rep(2060,3),
#'               sd = rep(10,3),
#'               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
#'
#'
#'cooling_pulse1(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(19,3),
#'               time_peak = rep(2060,3),
#'               sd = rep(10,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'
#'#######################################################################
#'   #Example 4: Different peaks of temperature.
#'#######################################################################
#'
#'temp_peak1 <- 16
#'temp_peak2 <- 5/4*temp_peak1
#'temp_peak3 <- 5/4*temp_peak2
#'
#'
#'cooling_pulse1(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_ini = rep(28,3),
#'               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),
#'               sd = rep(10,3),
#'               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
#'
#'
#'cooling_pulse1(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_ini = rep(29,3),
#'               temp_cmin = rep(18,3),
#'               temp_cmax = rep(30,3),
#'               ro = rep(0.7,3),
#'               lambda = c(lambda1,lambda2,lambda3),
#'               temp_peak = rep(19,3),
#'               time_peak = rep(2060,3),
#'               sd = rep(10,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'}

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


cooling_pulse1<- function(y_ini = c(N = 400, N = 400, N = 400),
                          temp_ini = rep(35,3),
                          temp_cmin = rep(18,3),
                          temp_cmax = c(25,28,35),
                          ro = rep(0.7,3),
                          lambda = rep(0.00005,3),
                          temp_peak = rep(25,3),
                          time_peak = rep(2060,3),
                          sd = rep(2,3),
                          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] && temp_peak[2]<=temp_ini[2] && temp_peak[3]<=temp_ini[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){

P1E <- function (times,temp_a,temp_peak,time_peak,sd) {
  T <-  temp_a-(temp_a-temp_peak)*exp(-(times-time_peak)^{2}/(2*sd^{2}))

}


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

  temp_a1=(temp_ini[1]-temp_peak[1]*exp(-time_peak[1]^{2}/(2*sd[1]^{2})))/(1-exp(-time_peak[1]^{2}/(2*sd[1]^{2})))

time_op11=suppressWarnings(time_peak[1]+sqrt(-2*(sd[1])^2*log((temp_a1-temp_op1)/(temp_a1-temp_peak[1]))))
time_op12=suppressWarnings(time_peak[1]-sqrt(-2*(sd[1])^2*log((temp_a1-temp_op1)/(temp_a1-temp_peak[1]))))
time_cmin11=suppressWarnings(time_peak[1]+sqrt(-2*(sd[1])^2*log((temp_a1-temp_cmin[1])/(temp_a1-temp_peak[1]))))
time_cmin12=suppressWarnings(time_peak[1]-sqrt(-2*(sd[1])^2*log((temp_a1-temp_cmin[1])/(temp_a1-temp_peak[1]))))
suppressWarnings(sqrt(-2*(sd[1])^2*log((temp_a1-temp_cmin[1])/(temp_a1-temp_peak[1]))))
  ##########################################################

  temp_a2=(temp_ini[2]-temp_peak[2]*exp(-time_peak[2]^{2}/(2*sd[2]^{2})))/(1-exp(-time_peak[2]^{2}/(2*sd[2]^{2})))

time_op21=suppressWarnings(time_peak[2]+sqrt(-2*(sd[2])^2*log((temp_a2-temp_op2)/(temp_a2-temp_peak[2]))))
time_op22=suppressWarnings(time_peak[2]-sqrt(-2*(sd[2])^2*log((temp_a2-temp_op2)/(temp_a2-temp_peak[2]))))
time_cmin21=suppressWarnings(time_peak[2]+sqrt(-2*(sd[2])^2*log((temp_a2-temp_cmin[2])/(temp_a2-temp_peak[2]))))
time_cmin22=suppressWarnings(time_peak[2]-sqrt(-2*(sd[2])^2*log((temp_a2-temp_cmin[2])/(temp_a2-temp_peak[2]))))
  suppressWarnings(sqrt(-2*(sd[2])^2*log((temp_a2-temp_cmin[2])/(temp_a2-temp_peak[2]))))
  #########################################################

  temp_a3=(temp_ini[3]-temp_peak[3]*exp(-time_peak[3]^{2}/(2*sd[3]^{2})))/(1-exp(-time_peak[3]^{2}/(2*sd[3]^{2})))

time_op31=suppressWarnings(time_peak[3]+sqrt(-2*(sd[3])^2*log((temp_a3-temp_op3)/(temp_a3-temp_peak[3]))))
time_op32=suppressWarnings(time_peak[3]-sqrt(-2*(sd[3])^2*log((temp_a3-temp_op3)/(temp_a3-temp_peak[3]))))
time_cmin31=suppressWarnings(time_peak[3]+sqrt(-2*(sd[3])^2*log((temp_a3-temp_cmin[3])/(temp_a3-temp_peak[3]))))
time_cmin32=suppressWarnings(time_peak[3]-sqrt(-2*(sd[3])^2*log((temp_a3-temp_cmin[3])/(temp_a3-temp_peak[3]))))
suppressWarnings(sqrt(-2*(sd[3])^2*log((temp_a3-temp_cmin[3])/(temp_a3-temp_peak[3]))))
  ###############################################################
  # Time limits
  ##############################################################

  tm<-c(time_cmin11[1],time_cmin12[1],time_cmin21[1],time_cmin22[1],time_cmin31[1],time_cmin32[1])
  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_a1,temp_cmax[1],temp_op1,ro[1],lambda[1])
parms2<-c(temp_cmin[2],temp_ini[2],temp_a2,temp_cmax[2],temp_op2,ro[2],lambda[2])
parms3<-c(temp_cmin[3],temp_ini[3],temp_a3,temp_cmax[3],temp_op3,ro[3],lambda[3])
############################################################


    ##########################################################
    # Model for each trend
    ##########################################################

    model1 <- function (times, y,parms1) {
      with(as.list(c(y)), {
        T <- P1E(times,temp_a1,temp_peak[1],time_peak[1],sd[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 <- P1E(times,temp_a2,temp_peak[2],time_peak[2],sd[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 <- P1E(times,temp_a3,temp_peak[3],time_peak[3],sd[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 less than or equal to the initial temperature")
    }


    }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")
  }


}