Population Dynamics

Population dynamics is the study of fluctuations in the size and composition of populations. The population could be an entire species or a group of plants and animals living in a restricted area. Population could also reefer to the population of dollars living in an investment or the population of people with some property such as the population of people who have heard a rumor or are aware of some product.

There are several types of population growth. In exponential growth a population grows slowly at first, but then explodes and grows without limits. Logistical growth starts out like exponential growth but then levels off when the population hits the carrying capacity of the environment. The graph looks like an S-curve. This type of growth was explored in the rumor model. In cyclical growth the size of the population increases until the food supply is exhausted. The size then decreases giving time for the population of the food supply to increase and the cycle repeats.

Models/Biology/Wolf-Sheep Predation

In this model there are two breeds of turtles: wolves and sheep. Sheep move about randomly. They eat grass. If they can't get enough grass to eat, they die. If they have the energy, they reproduce. Wolves move about randomly trying to catch sheep. If they don't catch enough sheep, they die. If they have the energy, they reproduce.

We can see exponential growth in the sheep population by turning off grass and setting the initial number of wolves to zero.

We can get something like logistical growth if we turn on grass and set its regrowth time to something fast:

Cyclical growth is harder. Start with a population of 100 sheep, 50wolves, and grass turned off. Set the sheep reproduction rate to 3%. Experiment with the wold reproduction rate and gain from food to see if you can find a combination that produces a stable population of wolves.

Now turn grass on and watch the fluctuations in all three populations: