Escher: Air and Water

Halibut off the eastern seaboard are an endangered species. As a population problem the fish have a certain birth rate, a death rate and a more or less constant food supply and therefore a limiting population. The fish also have a predator, man, and the death rate is increased by the fishing rate. If we call the fishing rate, which is time dependent due to governmental regulation for example, dn then the fish population will be governed by

Pn+1 = (b - d - dn)Pn(1 - Pn/Mp) = (b - d)Pn(1 - Pn/Mp) - dnPn

a modified Logistic equation. Using a spread sheet add this fishing term dn to a column.

Questions:

1. How does the population behave as a function of time (generations, n)?
2. How does dn affect the generational population dependence?
3. Does the population fluctuate?
4. Is there chaos?
5. How might the model be improved?
6. Do the New England Fisheries Council scientists model the fish population and do they have any population data as a function of time. What models do they use?

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