Class Exercise I

Exploring Parameters

Both the Beverton-Holt and Ricker stock-recruitment curves have two parameters, a and b. These two parameters control the specific shape of each curve and dictate the peak level or recruitment, R_p, and, potentially, the stock level at which that peak will occur, S_p. In this exercise you will explore the relative effect of a and b on R_p and S_p, as well as the specific shape of the models.

The srSim() function in the FSAsim package can be used to create a graphic that shows the number of recruits (R) or the number of recruits per spawner (R/S) versus the number of spawners (S). This plot will have R_p and, for the Ricker curve, S_p labeled. A gear box allows you to choose values of a and b for each model to see how it affects the model curve, R_p, and, possibly, S_p. Use this function to answer the following questions. [Note that no arguments to srSim() are needed to show the Beverton-Holt model, but you must include type="Ricker" to show the Ricker model.]

1. How does changing a in the Beverton-Holt model effect R_p?
2. How does changing b in the Beverton-Holt model effect R_p?
3. How does changing a in the Ricker model effect R_p and S_p?
4. How does changing b in the Ricker model effect R_p and S_p?