Post on 11-Jan-2016
description
Can Marine Reserves bolster fishery
yields?
NO RESERVES
RESERVES (E = 0% outside)
Larvae-on-larvae density dependence
equal
0.2
0
0
0
00
Fraction protected
d/L
= 0
.01
d/L
= 0
.03
d/L
= 0
.1d
/L =
0.3
Traditional 3-Reserve network
Pre-dispersal
nand
Pre- or post-
dispersaln andN
0.4
0.4 0.8 0 0.4 0.8 0 0.4 0.8
Two size classes
Yie
ld
0.2
0.4
0.2
0.4
0.2
0.4
Post-dispersal
nand
Short disperser
Long disperser
Marine reserves can exploit population structure and life history in improving potential fisheries yieldsBrian 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.
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
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
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
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
Comparing MSYs:
MSYreserve = max{crLog[cr](1 – c) / g}
MSYfishable = max{ rNe-gN – N}
dYfishable/dN = re-gN – grNe-gN – 1 = 0
n 1 ProductLog
r
g
ProductLog[z] = w is the solution for z = wew
INCREASE
Costello and Ward. In Review.