Assigned Feb 10th
Due Feb 12th Beginning of Class
Population Models - Competition
In the shark model we discussed in class, we used a logistic model of population growth,
where the growth rate of population P in the absense of interspecies competition is
Now let us consider a more complex model,
in which the parameter c represents a minimum viable population level below which the growth rate
is negative. Assume that the coefficient of competition is 10-8 and that
the minimum viable population level is 3,000 for Black Tip Sharks and 15,000 for White Tip Sharks.
- Create a model using Python to explore the dynamics of this system.
- Can the two species of sharks coexist? Use analysitical analysis to find equlibrium points
(i.e. where do the differential equations equal 0?).
- Assume that there are currently 5,000 Black Tip Sharks and 70,000 White Tip Sharks. What does
this model predict about the future of the two shark populations?
- Suppose that we have underestimated the minimum viable population for the Black Tip Sharks, and
that it is actually closer to 10,000. Now what happens to the two species?