Population Dynamics

Logistic Growth

How many time periods?

Starting population
(100 to 500)

Ideal growth rate
(between 0 and 4)

About This Graph

Exponential growth cannot continue indefinitely. Eventually populations reach the limit of their resources. There is no more space to accomodate larger numbers or not enough food to support them. As they approach this limit the death rate increases or more individuals emigrate away and the population tends to level off. This pattern is referred to as logistic growth. The above graph lets you explore logistic growth by varying the initial population size and the growth rate. Enter new values in the text boxes and click the “Apply changes” button. You can also choose how far into the future you want to calculate by selecting one of the four time period buttons. Although this is a very simple model, careful choice of initial parameters can produce some surprisingly complex results.

The horizontal axis on the graph is the time axis and the vertical axis is the population size. Note that the scale on the vertical axis changes to match the calculated values. Pay close attention to the vertical scale when comparing graphs. You can mouse over points on the graph to read values for each point.

Time periods are arbitrary. The time axis just shows population change over time. No particular time units are used. You could assign different meanings to the time periods to suit your purpose. For bacteria that reproduce every twenty minutes, for example, each time period could be thought of as a twenty minute interval. For White-tailed Deer that typically give birth once a year, you might choose to think of a time period as a year.

Starting population is the number of individuals in the population at the beginning. The allowed range of from 100 to 500 individuals has been arbitrarily chosen to allow for some variety in explorations and to minimize artifacts resulting from mathematical simplifications.

Ideal growth rate is the rate of population increase when there are no limiting factors. However, as population increases, and the effects of limited space and food are felt, increasing death rate and emigration will reduce the overall growth rate.