marine reserves and fishery profit: practical designs offer optimal solutions
DESCRIPTION
Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara. Larval export. No Fishing. When is larval export maximized? - PowerPoint PPT PresentationTRANSCRIPT
Marine reserves and fishery profit: practical designs offer
optimal solutions.
Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara
Larval export
No Fishin
g
When is larval export maximized?
What reserve design (size and spacing) maximizes larval export to fishable areas?
Do reserves benefit fisheries?
Is fishery yield/profit greater under optimal reserve design than
attainable without reserves?
Research Question:
To maximize larval export (and thus benefit fisheries) should reserves be…
…few and large,
When is larval export maximized?
…or many and small?
SLOSS debate
Coastal fish & invert life history traits in model Adults are sessile, reproducing seasonally (e.g. Brouwer et al. 2003, Lowe et al. 2003, Parsons et al. 2003)
Larvae disperse, mature after 1+ yrs (e.g. Dethier et al. 2003, Grantham et al. 2003)
Larva settlement and/or recruitment success decreases with increasing adult density at that location
(post-dispersal density dependence) (e.g. Steele and Forrester 2002, Lecchini and Galzin 2003)
sy'all
txyxy
ty
ty
tx
tx
tx
tx
1tx RLK)FH(A)HM(AHAA
An integro-difference model describing coastal fish population dynamics:
Adult abundance at location x during time-step t+1
Number of adults
harvested
Natural mortality of adults that
escaped being harvested
Fecundity
Larval survival
Larval dispersal (Gaussian)(Siegel et al. 2003)
Larval recruitment at x
Number of larvae that successfully recruit to location x
Incorporating Density Dependence
Post-dispersal: )Hc(Ao
tx
tx
txeRR
sy'all
txyxy
ty
ty
tx
tx
tx
tx
1tx RLK)FH(A)HM(AHAA
Larva settlement and/or recruitment success decreases with increasing adult population density at that location.
FEW LARGE RESERVES
SEVERAL SMALL RESERVES
θ = 5
θ = 0
Cost of catching one fish
= Density of fish at that location
θ
θ = 5
θ = 0
Bottom line for fishermen:
Profit = Revenue - cost
Cost of catching one fish
= Density of fish at that location
θ
θ = 20
θ = 0
Bottom line for fishermen:
Profit = Revenue - cost
Cost of catching one fish
= Density of fish at that location
θ
FEW LARGE RESERVES
SEVERAL SMALL RESERVES
Scale bar = 100 km
Scale bar = 100 km
Scale bar = 100 km
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
Max Yield without Reserves
A spectrum of high-profit scenariosMax Yield without Reserves
A spectrum of high-profit scenarios
Cost = θ/density
Max Yield without Reserves
A spectrum of high-profit scenarios
Cost = θ/density (Stop fishing when cost = $1)
Max Yield without Reserves
A spectrum of high-profit scenarios
Cost = θ/density (Stop fishing when cost = $1)
Escapement = % of virgin K (K = 50)
Max Yield without Reserves
A spectrum of high-profit scenarios
Cost = θ/density (Stop fishing when cost = $1)
Escapement = % of virgin K (K = 50)
Zero-profit escapement level = θ/K = 40%
Max Yield without Reserves
A spectrum of high-profit scenarios
Cost = θ/density (Stop fishing when cost = $1)
Escapement = % of virgin K (K = 50)
Zero-profit escapement level = θ/K = 40%
Max Yield without Reserves
A spectrum of high-profit scenariosθ/K = 15/50 = 30%
Max Yield without Reserves
A spectrum of high-profit scenariosθ/K = 10/50 = 20%
Max Yield without Reserves
A spectrum of high-profit scenariosθ/K = 5/50 = 10%
Max Yield without Reserves
Summary 1. Post-dispersal density dependence generates larval
export.
2. Larval export varies with reserve size and spacing.
3. Fishery yield and profit maximized via…
Less than ~15% coastline in reserves
…Any reserve spacing option.
More than ~15% coastline in reserves
…Several small or few medium-sized reserves.
Summary
4. Reserves benefit fisheries when escapement is moderate to low (E < ~35%*K)
5. Reserves become more beneficial as fish become easier to catch (low θ)
Summary 4. Given optimal reserve spacing, a near-maximum
profit is maintained across a spectrum of reserve and harvest scenarios:
ReservesNone/few
Many
EscapementHigh Low
Summary
Along this spectrum exists an optimal reserve network scenario, based on the fisheries’ self-
regulated escapement, that maximizes profits to the fishery.
4. Given optimal reserve spacing, a near-maximum profit is maintained across a spectrum of reserve and harvest scenarios:
ReservesNone Many
EscapementHigh Low
None/few
University of California – Santa Barbara
National Science Foundation
THANK YOU!
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
Older, bigger fish produce many more young
Channel Islands
0 500 1000 15000
10
20
30
40
50Optimal Reserve Spacing
Distance between reserve centers [km]
Mea
n H
arv
est
Den
sity
[#
fis
h/k
m]
Reserve = 50% of the coastline
0 500 1000 15000
10
20
30
40
50Optimal Reserve Spacing
Distance between reserve centers [km]
Mea
n H
arv
est
Den
sity
[#
fis
h/k
m]
Dd = 100 kmDd = 200 kmDd = 300 km
Reserve = 50% of the coastline
FUTURE RESEARCH
1. Evaluate under post-dispersal dd where larvae recruitment success depends on sympatric larvae density.
2. Conduct analysis within a finite domain.
3. Add size structure to the fish population.
Scale bar = 100 km
Scale bar = 100 km
Marine reserves and fishery profit: practical designs offer
optimal solutions.
Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara
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.