Table of Contents

• The mystery
• 1. Introduction
• 2. The mystery
• 3. Exponential growth
• 4. Population dynamics
• 5. Exponential growth equation
• 6. You write the equation
• 7. Applet: Exp. growth
• 8. Summary of exp. growth
• 9. Assumptions about exp. growth
• 10. Applet: Once more with mortality
• 11. ...and an equation
• The plot thickens
• 12. Examining assumptions
• 13. Assumptions get violated
• 14. Carrying capacity...
• 15....mathematically expressed
• 16. Logistic growth
• 17. Applet: ... among elephants
• 18. Applet: ... among mice
• 19. Applet: ... among moths
• 20. Detour: chaotic dynamics
• 21. Applet: Seasonal changes
• 22. Applet: Disturbance = Death
• The case is cracked
• 23. You be the detective
• 24. Just the facts ma'am

Logistic growth

There is a name for this kind of growth that depends on the number of 'slots' left: logistic growth.

The major claim of the logistic growth model is this:

"the actual growth rate of the population is proportional to the percentage of slots available (as well as the current population size)"

In the exponential model, the growth rate was constant (i.e., every fly has 120 babies every month. No exceptions). This led to some pretty ridiculous results. With the logistic model, the growth rate varies according to what proportion of 'slots' are available. This will allow the output of the model to be much more realistic!!

 

So here's the entire equation: (you can roll over it to get some hints).