In gauravsk/ecoevoapps: Simulate Dynamics of Ecology/Evolution Models

Exponential growth

The following code simulates the dynamics of a population with exponential growth in continuous time.

# Import libraries
library(deSolve)

# Define a function for exponential growth
exponential_growth <- function(time,init,params) {
  with (as.list(c(time,init,params)), {
    # description of parameters:
    # r = per-capita growth rate of the focal species
    # N1 = population size of the focal species
    dN1 <- (r*N1)
    return(list(c(dN1)))
  })
}

# Define initial values
init <- c(N1 = 10)
params <- (r = 0.15)

# Define the time series over which to simulate dynamics
time <- 0:100

# Use deSolve::ode to run the model using defined parameters
population_dynamics <- 
  data.frame(deSolve::ode(func = exponential_growth,
                          y = init, times = time, parms = params))

# Make a simple plot of population size over time
plot(population_dynamics$N1~population_dynamics$time, type = "l")

Logistic growth

To simulate the logistic model, we simply need to modify the function and define the new parameter K:

# Import libraries
library(deSolve)

# Define a function for logistic growth
logistic_growth <- function(time,init,params) {
  with (as.list(c(time,init,params)), {
    # description of parameters:
    # r = per-capita growth rate of the focal species
    # N1 = population size of the focal species
    # K = carrying capacity of the focal species
    dN1 <- (r*N1)*(1-N1/K)
    return(list(c(dN1)))
  })
}

# Define initial values
init <- c(N1 = 10)
params <- c(r = 0.1, K = 500)

# Define the time series over which to simulate dynamics
time <- 0:100

# Use deSolve::ode to run the model using defined parameters
population_dynamics <- 
  data.frame(deSolve::ode(func = logistic_growth,
                          y = init, times = time, parms = params))

# Make a simple plot of population size over time
plot(population_dynamics$N1~population_dynamics$time, type = "l")

Lagged logistic growth

Running the lagged-logistic model requires the use of the function `deSove::lagvalue, which gives access to past (lagged) values of state variables, and the function deSolve::dede which, unlike deSolve::ode allows us to simulate delayed-differential equations:

lagged_logistic_growth <- function(time, init, params) {
  with (as.list(c(time,init,params)), {
    # description of parameters:
    # r = per-capita growth rate of the focal species
    # N1 = population size of the focal species
    # K = carrying capacity of the focal species
    # tau = time lag of density dependence

    tlag <- time - tau
    if (tlag < 0) {
      Nlag <- N1
    } else {
      Nlag <- deSolve::lagvalue(tlag)
    }
    dN1 <- r * N1 * (1-(Nlag/K))
    return(list(c(dN1)))
  })
}

init <- c(N1 = 50)
params <- c(r = 0.7, K = 500, tau = 2.2)

# Define the time series over which to simulate dynamics
time <- 0:200

# Use deSolve::ode to run the model using defined parameters
population_dynamics <- 
    data.frame(deSolve::dede(func = lagged_logistic_growth,
                 y = init, times = time, parms = params))

# Make a simple plot of population size over time
plot(population_dynamics$N1~population_dynamics$time, type = "l")

gauravsk/ecoevoapps documentation built on July 9, 2024, 9:37 p.m.