epcc (version 1.4.7)

increasing_linear: Projection of increasing linear temperature

Description

This function allows simulating the effect of a linear increase in environmental temperature on the abundance of ectotherm populations.

Usage

increasing_linear(
  y_ini = c(N = 100, N = 200, N = 400),
  temp_ini = rep(26, 3),
  temp_cmin = rep(18, 3),
  temp_cmax = rep(40, 3),
  ro = rep(0.7, 3),
  m = rep(0.15, 3),
  lambda = rep(5e-05, 3),
  time_start = 2005,
  time_end = 2100,
  leap = 1/12
)

Arguments

y_ini

Initial population values (must be written with its name: N).

temp_ini

Initial temperature.

temp_cmin

Minimum critical temperature.

temp_cmax

Maximum critical temperature.

ro

Population growth rate at optimum temperature.

m

Temperature trend growth slope.

lambda

Marginal loss by non-thermodependent intraspecific competition.

time_start

Start of time sequence.

time_end

End of time sequence.

leap

Time sequence step.

Value

(1) A data.frame with columns having the simulated trends.

(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.

Details

Three populations and/or scenarios can be simulated simultaneously. The temperature trend is determined by a linear function. The slope 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).

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

Examples

# NOT RUN {
#######################################################################
  #Example 1: Different initial population abundances.
#######################################################################

increasing_linear(y_ini = c(N = 100, N = 200, N = 400),
                 temp_ini = rep(26,3),
                 temp_cmin = rep(18,3),
                 temp_cmax = rep(40,3),
                 ro = rep(0.7,3),
                 m = rep(0.15,3),
                 lambda = rep(0.00005,3),
                 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_linear(y_ini = c(N = 100, N = 100, N = 100),
                 temp_ini = rep(26,3),
                 temp_cmin = c(temp_cmin1,temp_cmin2,temp_cmin3),
                 temp_cmax = c(temp_cmax1,temp_cmax2,temp_cmax3),
                 ro = rep(0.7,3),
                 m = rep(0.15,3),
                 lambda = rep(0.00005,3),
                 time_start = 2005,
                 time_end = 2100,
                 leap = 1/12)
# }
# NOT RUN {
#######################################################################
  #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_linear(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),
                 m = rep(0.15,3),
                 lambda = rep(0.00005,3),
                 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_linear(y_ini = c(N = 100, N = 100, N = 100),
                 temp_ini = rep(26,3),
                 temp_cmin = rep(18,3),
                 temp_cmax = rep(36,3),
                 ro = rep(0.7,3),
                 m = rep(0.15,3),
                 lambda = c(lambda1,lambda2,lambda3),
                 time_start = 2005,
                 time_end = 2100,
                 leap = 1/12)
# }