Fluctuating_pop_dynamics

Examples of delayed density-dependent dynamics

Sable fluctuations

# Parameters
r <- 0.6   # Intrinsic growth rate
K <- 80   # Carrying capacity
tau <- 2.4/r  # Time delay in generations
generations <- 200  # Total number of generations to simulate

# Initial population size
N <- numeric(generations)
N[1:tau] <- 1  # Start with a small population size for the first few generations

# Simulating the delayed density dependence
for (t in (tau + 1):generations) {
  N[t] <- N[t - 1] * exp(r * (1 - N[t - tau] / K))
}


# Plotting the population over time
plot(1:generations, N, type="o", col="blue", lwd=2,
     main="Population Growth with Delayed Density Dependence",
     xlab="Generation", ylab="Population Size")
abline(h = 80, col = "red", lty ="dashed")
rt = r * tau
mtext(text = paste0("r  = ", r, ", ", "tau =", tau, ", ", "r*tau = ", round(rt, 2)),  col = "red", cex = 1.2)

Dampened dynamics

# Parameters
r <- 0.6   # Intrinsic growth rate
K <- 80   # Carrying capacity
tau <- 1.8/r  # Time delay in generations
generations <- 200  # Total number of generations to simulate

# Initial population size
N <- numeric(generations)
N[1:tau] <- 1  # Start with a small population size for the first few generations

# Simulating the delayed density dependence
for (t in (tau + 1):generations) {
  N[t] <- N[t - 1] * exp(r * (1 - N[t - tau] / K))
}

# Plotting the population over time
plot(1:generations, N, type="o", col="blue", lwd=2,
     main="Population Growth with Delayed Density Dependence",
     xlab="Generation", ylab="Population Size")
abline(h = 80, col = "red", lty ="dashed")
rt = r * tau
mtext(text = paste0("r  = ", r, ", ", "tau =", tau, ", ", "r*tau = ", round(rt, 2)),  col = "red", cex = 1.2)

Logistic model with K

# Parameters
r <- 0.6   # Intrinsic growth rate
K <- 80   # Carrying capacity
tau <- 1  # Time delay in generations
generations <- 50  # Total number of generations to simulate

# Initial population size
N <- numeric(generations)
N[1:tau] <- 1  # Start with a small population size for the first few generations

# Simulating the delayed density dependence
for (t in (tau + 1):generations) {
  N[t] <- N[t - 1] * exp(r * (1 - N[t - tau] / K))
}

# Plotting the population over time
plot(1:generations, N, type="o", col="blue", lwd=2,
     main="Population Growth with Delayed Density Dependence",
     xlab="Generation", ylab="Population Size")
abline(h = 80, col = "red", lty ="dashed")
rt = r * tau
mtext(text = paste0("r  = ", r, ", ", "tau =", tau, ", ", "r*tau = ", round(rt, 2)),  col = "red", cex = 1.2)