Week 5 Homework List

As always, a self contained ipynb solutions should be uploaded to Canvas along with a pdf copy. Each Question shall be clearly displayed inside the same notebook. Headers and formating will be graded

Note:

Use a modified Rickers Equation to answer the following questions about fish population.

$$ X_{n+1} = \Gamma(1,0.1) X_{n} e^{r_0(1-\frac{X_n}{K})} $$

where $\Gamma(1,0.1)$ is a noise variable with normal distribution centered at 1 and standard deviation of 0.1.

Each time step is another year

Until stated you can assume that $K=10000, r_0 =0.3$

Question 1

Plot various(1000+) solutions on the same figure to illustrate how the noise can vary the solutions. You can assume that your starting fish population is 100 fish

Question 2

After 5 years what range of fish would you expect to have if you started with

  • 10 fish
  • 100 fish
  • 500 fish
  • 1,000 fish
  • Question 3

    After 30 years, do you expect a larger distribution with higher growth rate or lower growth rate, you can assume $r_0 \in (0,1)$. Back this up with graphs and/or data.