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An Introduction to Population Ecology - Harvesting the Explosion-Extinction Model

Brandon M. Hale and Maeve L. McCarthy
Since the Explosion-Extinction Model can be used to represent the effects of an introduced species on indigenous species, we can also use it to calculate the percentage of harvesting necessary to eradicate an introduced species. In particular (Edwards & Penney, 1999) we can modify the Explosion-Extinction equation by subtracting a harvesting term, hP:


You can investigate the effect of this harvesting by returning to the main window, selecting both the Explosion-Extinction radio button and the Include Harvesting checkbox, and then clicking OK. (If the maplet is not running, use the button at the right to start it again.) If = 0, everything works just like the normal Explosion-Extinction Model. Remember, h is the percentage of the population that is hunted or captured, expressed as a decimal fraction.


  1. The default values are P0 = 20 units, M = 8 units, r = 0.04 per year and stop time = 100 years. Graph the population. What happens when you introduce a harvesting percentage of 7.5%?
  2. Try increasing the initial population. What happens? What is the smallest population that does not become extinct at this harvesting level? How would you summarize the effect of harvesting on the minimum sustainable level?
  3. Twenty individuals of an r-dependent species have been introduced into an area without its natural predators. The introduced species is known to increase rapidly at a rate of 40% per year, and it requires a population of only 8 individuals to maintain an increasing population. What percentage of the population must be hunted or captured in order to remove the introduced species?

Brandon M. Hale and Maeve L. McCarthy, "An Introduction to Population Ecology - Harvesting the Explosion-Extinction Model," Loci (October 2005)


Journal of Online Mathematics and its Applications