anm.geo.growth: Animated depictions of population growth

Description

Animated depictions of geometric, exponential, and logistic growth.

Usage

anm.geo.growth(n0, lambda, time = seq(0, 20), ylab = "Abundance",
xlab = "Time", interval = 0.1, ...)
anm.exp.growth(n, rmax, time = seq(0, 20), ylab = "Abundance", 
xlab = "Time", interval = 0.1, ...)
anm.log.growth(n, rmax, K, time = seq(0, 60), ylab = "Abundance", 
xlab = "Time", interval = 0.1, ...)
anm.geo.growth.tck()
anm.exp.growth.tck()
anm.log.growth.tck()

Arguments

n0: Population size at time zero for geometric population growth.
lambda: Geometric growth rate.
time: A time sequence, i.e. a vector of integers which must include 0.
ylab: Y-axis label.
xlab: X-axis label
interval: Animation interval in seconds per frame.
...: Additional arguments to plot
n: Initial population numbers for exponential and logistic growth
rmax: The maximum intrinsic rate of increase
K: The carrying capacity

Author

Ken Aho

Details

Presented here are three famous population growth models from ecology. Geometric, exponential and logistic growth. The first two model growth in the presence of unlimited resources. Geometric growth is exponential growth assuming non-overlapping generations, and is computed as:

$$N_t = N_{0}\lambda^t,$$

where $N_t$ is the number of individuals at time y, $\lambda$ is the geometric growth rate, and t is time.

Exponential growth allows simultaneous existence of multiple generations, and is computed as:

$$\frac{dN}{dt}=r_{max}N,$$

where $r_{max}$ is the maximum intrinsic rate of increase, i.e. max(birth rate - death rate), and N is the population size. With logistic growth, exponential growth is slowed as N approaches the carrying capacity. It is computed as:

$$\frac{dN}{dt}=r_{max}N\frac{K-N}{K},$$

where $r_{max}$ is the maximum rate of intrinsic increase, $N$ is the population size, and $K$ is the carrying capacity

Package tcltk allows implementation of all three models using GUIs.

Examples

Run this code

if (FALSE) {
anm.geo.growth(10,2.4)
}