Calculating “r” from a Published Data Set (4A)

Comment on the biological meaning of the r value you have calculated:

I calculated the r value to be .378 (using data points 1985, 5.4 and 1994, 8.8). As this number is larger than zero, it indicates that the Egyptian goose population in the Netherlands has been growing (their birth rate exceeds their death rate), and will continue to do so. It is likely that something will end up limiting the growth of these geese, be it predators or competitors. Eventually the population should reach a stable size near the carrying capacity of the habitat.

Questions:

1. In the exponential population growth equation, N_t=N₀(e^rt), identify what each of the symbols stands for and explain whether it is a variable or a constant.
   • N_t is the population at the time you choose; it is a variable. N₀ is the initial population; it is a constant. “e” is a mathematical constant equal to about 2.718. “r” is the intrinsic rate of growth of a population and is constant. “t” stands for time which is variable.
2. Use the value of r you calculated to project the number of geese in 1994. Does the calculated number approximate the number actually observed in 1994? Explain any discrepancies you encounter.
   • The population estimate for 1994 using the equation is 7,776. This is higher than the observed number. This may be because the habitat is reaching its carrying capacity, or it could be a result of human error in the collection of data. It may also be caused by an increase in predation as the community adjusts to the insertion of the geese.
3. Why is the method used for calculating r more reliable than choosing two points from the data table?
   • The method we used is better because two points on the table may not fall directly on the line of best fit. The line of best fit is a better representation of the overall pattern than any two points on the data table.
4. Why do you think Egyptian goose populations are increasing exponentially in the Netherlands, but not in Africa where they originated.
   • The Netherlands likely has more available habitat and fewer natural predators than the native habitat in Africa.
5. Can you name an example of an exotic species that has become an ecological problem in North America, and explain why this species is an ecological threat?
   • The Brazilian Pepper tree, found in Florida, is an introduced species that is an ecological threat because it spread rapidly and overpowered mangroves, which are an important species in Florida, and can invade mature canopies, choking out most other plants.