STEP@USF

The Allee effect (1931) describes the phenomena that for smaller populations, the reproduction and survival of individuals decrease, due to the lack of suitable mates. Alternatively, it can be thought of as a positive correlation between population density and the per capita growth rate. Determine at what population densities you expect to see the Allee effect and at what threshold density does is the Allee effect become negligible.

Theory:

• Logistic equation (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 346)
• Allee effect (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 382)

References:

Many threatened species face extinction risks due to loss of habitat, disease, hunting pressure, etc., which ultimately result in dangerously low population sizes. Choose a threatened species with an extinction risk and create an equation/model that describes the change in their population size over time. At the current population growth rate, how long would it take for the population to go extinct. How much would the population growth rate or how many additional individuals would have to immigrate into the population for the population to avoid extinction?

Theory

• logistic equation (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 364-366)

References

In some populations there is no distinct breeding season, so reproduction takes place continually, which can make it problematic to keep track of all the new births. Create a model/equation that would enable you to take a census of the number of newborns over time of a continuously breeding population of your choice. Assume that juveniles and old females cannot reproduce. How would this change your model/equation?

Calculus techniques used:

• Integration

Theory:

• Age structured populations (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 424)
• Applications of integration (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 399)

References:

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