can marine reserves bolster fishery yields?

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.