1. EBM: Control Freaks Model Zero: Two interacting species and a regulator who is informationally challenged

2. “Real world”: two-species competition

3. Optimal control problem of the informationally challenged regulator Regulator is choosing effort levels over time to max. profits from fishing each species Assumption is that the regulator does not know the interactions between the species  is the (social) discount rate

4. What do I do… I solve for the optimal effort level at the steady-state, that is, the solution to optimal control problem at the equilibrium. Let, this effort level be E i ss Take E i ss, which is a constant, and plug it into the real world two-species model

5. “Real world”: two-species competition This generates a path of fish stocks Assumption: Manager does not change the policy over time

6. Comparison to case with no- interaction I compare these population trajectories to the ones I get from the following:

7. Experiment 1 Only fish x 1, f 1 >0, f 2 =0 Look at different levels of the competition term that is assumed equal to each other (  i =  ) –Low:  –Medium:  –High:  –where  is equal to 70% of r i =r Measure stock in terms of density (with all adjustments to parameter levels)

8. Red line is what the regulator is believing to occur, Blue line is fished population, Green is unfished

9. Experiment 2 Everything the same, but now we are fishing in both patches f 1 >0, f 2 >0 (as defined previously) Look at different levels of the competition term that is assumed equal to each other (  i =  ) –Low:  –Medium:  –High:  –where  is equal to 70% of r i =r

10. Red line is what the regulator is believing to occur

11. Preliminary conclusions w/ competition Fishing both species seems to lower the absolute interaction strength (even though the alpha term is the same) –Absolute interaction strength  x  x  Results are, of course, specific to the parameter set We should determine if we could derive these results analytically

12. Now, looking at predator-prey

13. Experiment 1 Fishing the prey (f 1 >0) not the predatory All other parameters the same as with competition Natural mortality of predator=.01*r 1

14. Fished population is the prey, Predator is unfished and red is what the regulator “sees”

15. Experiment 2 Fishing the predator (f 1 >0) not the prey All other parameters the same as with competition Natural mortality of predator=.01*r 1

16. Fishing the predator and not the prey

17. Experiment 3 Fishing the predator and the prey (f i >0) All other parameters the same as with competition Natural mortality of predator=.01*r 1

18. Fishing both predator (x 2 ) and prey (x 1 )

19. To do… Analytics of this very special setting More sensitivity analysis