Population Growth – Exponential and Logistic Models vs. Complex Reality

This analysis and discussion activity is designed to help students develop a solid understanding of the exponential and logistic models of population growth, including the biological processes that result in exponential or logistic population growth. Students learn about the simplifying assumptions built into the exponential and logistic models and explore how deviations from these assumptions can result in discrepancies between the predictions of these models and the actual trends in population size for natural populations. This activity is designed to help students meet the Next Generation Science Standards and the Common Core State Standards.

The first two attached files have the version of the Student Handout that engages students in understanding the mathematical formulae for the exponential and logistic models of population growth, as well as evaluating the relative advantages of graphs and mathematical formulae as models of population growth (first file is a Word document and second file is a PDF). The third attached file has the version of the Student Handout that omits the mathematical formulae. The fourth attached file has the Teacher Notes for this activity.

PopGrowthMath SHO.docx1.64 MB
PopGrowthMath SHO.pdf450.49 KB
PopGrowthBio SHO.docx1.74 MB
PopGrowth TN.docx52.59 KB


Gamal Sherif's picture

Rabbits and genetic variability

re: "Rabbits can also show exponential population growth. A female cottontail rabbit begins reproducing by one year of age and typically has 3-4 litters of 4-5 baby rabbits each breeding season. A cottontail rabbit can live up to 8 years in captivity. If a population begins with a pair of breeding adults, and the rabbits have maximum reproduction and survival, how many rabbits do you think there would be after six years (just guessing, without calculating)?"

Why is it that the rabbits' offspring can interbreed with little or no mutation? Is there enough genetic variability so that the offspring from the first pair of rabbits are able to successfully produce healthy offspring?

iwaldron's picture

Perils of Inbreeding

Thank you for your interesting comment which makes an important point. In fact, inbreeding rabbits in the way proposed would be expected to result in substantial problems. Breeding advice for rabbits often suggests various types of close inbreeding (e.g. parent/offspring, which is called "linebreeding"); however, this advice emphasizes the importance of culling any offspring which have inherited defects.

It is interesting that the huge population of rabbits in Australia is believed to be descendents of an initial group of 24 wild rabbits. This suggests that this small population had sufficient genetic variability to produce a very healthy population, although there may well have been additional introductions of rabbits since 1859. Also, of course, natural selection accomplished the recommended culling.

Your comment and these observations suggest another point that would be useful to include in the discussion of the last question in the section on Exponential Population Growth about unrealistic assumptions in the hypothesized rabbit population example.

iwaldron's picture

2014 revisions

Some of the questions in the Student Handout have been revised and reorganized to improve clarity, and a question on density-dependent vs. density-independent effects on population growth has been added. The Teacher Notes have been substantially expanded to include more background information and explanation, as well as additional links to related learning activities for teaching ecology.

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