Exercise 5. Constant harvest and constant effort harvest. (15 points total) Now lets explicity add harvest to the logistic growth equation. Constant harvest rate H: N(t + 1) = N(t) + r * N(t) * (1 - N(t)/K) - H Constant effort harvest with fishing mortality F: N(t + 1) = N(t) + r * N(t) * (1 - N(t)/K) - F * N(t) We can again set our r, K and N0 values. We'll start the population at carrying capacity r <- 0.3 K <- 500 N0 <- 500

C. Now simulate the population under fishing mortality of F = 0.2, 0.3, 0.4 and graph the output of N(t) through time (3 points) Describe the results

D. Plot dN/dt and the three F values on the same plot. (3 points) Hint: Use the abline() function to make lines with intercept 0 and slope

F. You can use the lty option to make the lines dashed or dotted if you so choose and the lwd option to change the line width. Label the axes. Describe the relationship between the graphs in parts C and D. How do the graphs in D tell you what the graphs in C must do