asbio (version 1.0-5)

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

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 assumes 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 existience 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 Installation of package tcltk allows implementation of all three models using GUIs.

See Also

anm.LVexp, anm.LVcomp

Examples

anm.geo.growth(10,2.4)