Copyright 1997 by Mark Janeba
Goals: Learning how to:
BigIsland, off the southern coast of Freedonia, had a native population of Farnsworth's Sparrows that was wiped out by hunters in the late 1800's. It seems that the Farnsworth's Sparrow, when stuffed, made a popular centerpiece on dining room tables of that time and region.
In the 1930's, the Freedonian Audobon society discovered a small population of Farnsworth's Sparrows in a remote corner of Freedonia. Some were captured to transport to Big Island, in order to re-establish the species in that habitat.
Since there were no natural predators for Farnsworth's Sparrows on Big Island, and since hunting them was banned, their population grew unhindered. Like most species in such an environment, their growth rate was jointly proportional to the population size and the rate at which food became available in the habitat. Food plants for Farnsworth's Sparrows grows at a constant rate on Big Island, but much of it is not available to new sparrows because existing sparrows eat it. Consequently, the rate at which food becomes available is C-k*(size of Farnsworth's Sparrow population). In 1935, it is estimated there were 1050 Farnsworth's Sparrows on the island, and with the birthrate exceeding the death rate by 200 per year. In 1939, the population had grown to 2100, and was growing by 330 birds per year. During the war years, no data was taken.
It is almost certain that the Farnsworth's Sparrow population on Big Island would be secure today, if the Freedonian government had not allowed the development of the island starting in 1946. This move, taken due to population pressure on the mainland, brought another feared predator to the island, house cats.
Remarkably, it only took a year for the government to decide another catastrophe was in the making, and prohibited the ownership of cats on the island. It was hoped that the few stray cats could be quickly rounded up. Due to the rugged nature of the west end of the island, this was not to be.
The feral cats that now roam this end of the island compete with each other for food. Therefore the cat population's growth rate is the sum of two terms: The first is a negative number times the cat population (more cats makes the growth rate less). The second term is proportional to the catfood supply, where here "catfood" means anything cats will eat. Catfood has consisted pretty much entirely of Farnsworth's Sparrows. However, since a sparrow does not become catfood until the kitty encounters the bird, and since these encounters become more likely as the cat population grows, the bird's contribution to the catfood supply is jointly proportional to the bird population and the cat population.
Since the sparrow population is now much less than it would be without cats, the bird population's birth rate is pretty much proportional to population size. Birdfood is now so plentiful due to reduced bird population that food supply (or lack of it) doesn't affect bird birthrate much. However, the bird death rate is pretty much the number of cat-bird encounters, which is again jointly proportional to the bird population and the cat population.
By January 1949, the feral cat population was at 120, and rising at 16 cats/year. The Farnsworth's sparrow population was 2330, and falling at the alarming rate of 3030 birds/year.
One year later, the feral cat population was at 87, and falling at 45 cats/year. The Farnsworth's sparrow population was 705, and falling at the rate of 451 birds/year.
Your report will be evaluated for its clarity, completeness, and correctness, with a bonus for thoughtful creativity. Clarity means that another calculus student who was not assigned this project must be able to understand your report as well as s/he may desire. Completeness means that such a student must not have any further questions about your methods, since the report explains them carefully in the first place. Completeness also means no obvious issues were overlooked.
Your full report is due at 5 p.m., May 2nd, at the Freedonian Office of Ecological History, 203 Collins Hall. Anything slipped under the door after the secretary leaves at 5 p.m. will be too late and will not be accepted.
Please mail comments or questions to: mjaneba@willamette.edu