Can Marine Reserves bolster fishery yields?

1. Can Marine Reserves bolster fishery yields?

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

4. 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. Short disperser Post-dispersal density dependence: survival of new recruits decreases with increasing density of adults at settlement location. Long disperser

6. Logistic model: post-dispersal density dependence No reserves: Nt+1 = Ntr(1-Nt) Yield = Ntr(1-Nt)-Nt 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: Nt+1 = crNr(1-Nr) Nr* = 1 – 1/cr Yield = crNr(1 – c)(1 – No) Yield(Nr* = 1 – 1/cr) = -rc2 + 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: Nt+1 = rNte-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: Nr = crNre-gNr Nr* = Log[cr] / g Recruitment to fishable domain = Yield = crNr(1 – c)e-gNo Yield(Nr* = 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: MSYreserve = max{crLog[cr](1 – c) / g} MSYfishable = max{ rNe-gN – N} dYfishable/dN = re-gN – grNe-gN – 1 = 0 ProductLog[z] = w is the solution for z = wew

17. INCREASE

18. Costello and Ward. In Review.