R/trend_periodic.R

In epcc: Simulating Populations of Ectotherms under Global Warming

#' Periodic temperature trend
#'
#' @description This function allows simulating the effect of a periodic temperature
#'              trend 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 optimum 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 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 trigonometric function characterized
#'         by amplitude and period. 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.
#'#######################################################################
#'
#'trend_periodic(y_ini = c(N = 100, N = 200, N = 400),
#'               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(0.2,3),
#'               B = rep(0.6,3),
#'               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
#'
#'trend_periodic(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),
#'               A = rep(2,3),
#'               B = rep(0.6,3),
#'               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 <- 35
#'
#'# 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
#'
#'trend_periodic(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),
#'               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
#'
#'trend_periodic(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 = c(lambda1,lambda2,lambda3),
#'               A = rep(2,3),
#'               B = rep(0.6,3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'
#'#######################################################################
#'   #Example 5: Different wave amplitudes.
#'#######################################################################
#'
#'A3 <- 4
#'A2 <- 1/2 * A3
#'A1 <- 1/2 * A2
#'
#'trend_periodic(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_ini = rep(25,3),
#'               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),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'
#'#######################################################################
#'   #Example 6: Different periods.
#'#######################################################################
#'
#'B3 <- pi/5
#'B2 <- 1/2 * B3
#'B1 <- 1/2 * B2
#'
#'trend_periodic(y_ini = c(N = 100, N = 100, N = 100),
#'               temp_cmin = rep(18,3),
#'               temp_ini = rep(22,3),
#'               temp_cmax = rep(35,3) ,
#'               ro = rep(0.7,3),
#'               lambda = rep(0.00005,3),
#'               A = rep(2,3),
#'               B = c(B1,B2,B3),
#'               time_start = 2005,
#'               time_end = 2100,
#'               leap = 1/12)
#'}
###################################################


trend_periodic<- 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),
                          A = rep(0.5,3),
                          B = rep(0.35,3),
                          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]){


  u1<- temp_ini[1]-temp_cmin[1]
  v1<- temp_cmax[1]-temp_ini[1]
  if(u1<=v1){
    p1<-u1
  }else{
    p1<-v1
  }

  u2<- temp_ini[2]-temp_cmin[2]
  v2<- temp_cmax[2]-temp_ini[2]
  if(u2<=v2){
    p2<-u2
  }else{
    p2<-v2
  }

  u3<- temp_ini[3]-temp_cmin[3]
  v3<- temp_cmax[3]-temp_ini[3]
  if(u3<=v3){
    p3<-u3
  }else{
    p3<-v3
  }

  if(abs(A[1])<= p1 || abs(A[2])<= p2 || abs(A[3])<= p3){



P <- function (times,temp_ini,A,B) {
  T <- temp_ini+A*sin(B*(times-time_start))

}


##########################################################
# 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],A[1],B[1])
parms2<-c(temp_cmin[2],temp_ini[2],temp_cmax[2],temp_op2,ro[2], lambda[2],A[2],B[2])
parms3<-c(temp_cmin[3],temp_ini[3],temp_cmax[3],temp_op3,ro[3], lambda[3],A[3],B[3])

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


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

    model1 <- function (times, y,parms1) {
      with(as.list(c(y)), {
        T <- P(times,temp_ini[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 <- P(times,temp_ini[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 <- P(times,temp_ini[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")
#############################################################


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

q1 <- 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[length(times)]),aes(x=.data$x,
                                            ymax=.data$y),ymin=0,alpha=0.3, fill="brown") +
geom_ribbon(data=subset(dat2,times>times[1] & times<times[length(times)]),aes(x=.data$x,
                                           ymax=.data$y),ymin=0,alpha=0.3, fill="green4") +
geom_ribbon(data=subset(dat3,times>times[1] & times<times[length(times)]),aes(x=.data$x,
                                            ymax=.data$y),ymin=0,alpha=0.3, fill="blue") +
geom_line(data =subset(data1,times>times[1] & times<times[length(times)]), color = "brown")+
geom_line(data =subset(data2,times>times[1] & times<times[length(times)]), color = "green4")+
geom_line(data =subset(data3,times>times[1] & times<times[length(times)]), 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)")


q2 <- ggplot(data, aes(x=.data$x, y=.data$y)) +
theme_bw()+
theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank())+
geom_line(data =subset(da1,times>times[1] & times<times[length(times)]), color = "brown")+
geom_line(data =subset(da2,times>times[1] & times<times[length(times)]), color = "green4")+
geom_line(data =subset(da3,times>times[1] & times<times[length(times)]), 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(q1, q2)


  }else{
    stop("The absolute value of |A| must be less with the intention that the temperature trend is within the tolerance range of the organism")
  }

  }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")
  }



}