1. Can Marine Reserves bolster fishery yields?

2. NO RESERVES RESERVES (E = 0% outside) Larvae-on- larvae density dependence equal

4. Short disperser Long disperser Marine reserves can exploit population structure and life history in improving potential fisheries yields Brian Gaylord, Steven D. Gaines, David A. Siegel, Mark H. Carr. In Press. Ecol. Apps. Post-dispersal density dependence: survival of new recruits decreases with increasing density of adults at settlement location.

6. Logistic model: post-dispersal density dependence No reserves: N t+1 = N t r(1-N t ) Yield = N t r(1-N t )-N t MSY = max{Yield} dYield/dN = r – 2rN – 1 = 0 N = (r – 1)/2r MSY = Yield(N = (r – 1)/2*r) = (r – 1) 2 / 4r

7. Logistic model: Scorched earth outside reserves post-dispersal density dependence Reserves: N t+1 = crN r (1-N r ) N r * = 1 – 1/cr Yield = crN r (1 – c)(1 – N o ) Yield(N r * = 1 – 1/cr) = -rc 2 + cr + c – 1 dYield/dc = -2cr + r + 1 = 0 c = (r + 1)/2r MSY = Yield(c = (r + 1)/2r) = (r – 1) 2 / 4r

9. Ricker model: post-dispersal density dependence No reserves: N t+1 = rN t e -gNt Surplus growth = Yield = rNe -gN – N dYield/dN = re -gN – grNe -gN – 1 = 0 1. Find N for dYield/dN = 0 2. Plug N into Yield(N,r,g) = MSY

12. Ricker model: Reserves: N r = crN r e -gNr N r * = Log[cr] / g Recruitment to fishable domain = Yield = crN r (1 – c)e -gNo Yield(N r * = Log[cr] / g) = crLog[cr](1 – c) / g dYield/dc = (rLog[cr] + r – 2crLog[cr] – cr) / g = 0 1. Find c for dYield/dc = 0 2. Plug c into Yield(c,r,g) = MSY

16. Comparing MSYs: MSY reserve = max{crLog[cr](1 – c) / g} MSY fishable = max{ rNe -gN – N} dY fishable /dN = re -gN – grNe -gN – 1 = 0 ProductLog[z] = w is the solution for z = we w

17. INCREASE

18. Costello and Ward. In Review.