Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce...
-
date post
20-Dec-2015 -
Category
Documents
-
view
215 -
download
1
Transcript of Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce...
![Page 1: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/1.jpg)
Marine reserves and fishery profit: practical designs offer
optimal solutions.
Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara
![Page 2: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/2.jpg)
Larval export
No Fishin
g
![Page 3: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/3.jpg)
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?
![Page 4: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/4.jpg)
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
![Page 5: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/5.jpg)
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)
![Page 6: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/6.jpg)
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
![Page 7: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/7.jpg)
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.
![Page 8: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/8.jpg)
FEW LARGE RESERVES
SEVERAL SMALL RESERVES
![Page 9: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/9.jpg)
θ = 5
θ = 0
Cost of catching one fish
= Density of fish at that location
θ
![Page 10: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/10.jpg)
θ = 5
θ = 0
Bottom line for fishermen:
Profit = Revenue - cost
Cost of catching one fish
= Density of fish at that location
θ
![Page 11: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/11.jpg)
θ = 20
θ = 0
Bottom line for fishermen:
Profit = Revenue - cost
Cost of catching one fish
= Density of fish at that location
θ
![Page 12: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/12.jpg)
FEW LARGE RESERVES
SEVERAL SMALL RESERVES
![Page 13: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/13.jpg)
Scale bar = 100 km
![Page 14: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/14.jpg)
Scale bar = 100 km
![Page 15: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/15.jpg)
Scale bar = 100 km
![Page 16: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/16.jpg)
![Page 17: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/17.jpg)
![Page 18: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/18.jpg)
![Page 19: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/19.jpg)
![Page 20: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/20.jpg)
![Page 21: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/21.jpg)
![Page 22: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/22.jpg)
![Page 23: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/23.jpg)
![Page 24: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/24.jpg)
![Page 25: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/25.jpg)
![Page 26: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/26.jpg)
Max Yield without Reserves
![Page 27: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/27.jpg)
Max Yield without Reserves
![Page 28: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/28.jpg)
Max Yield without Reserves
![Page 29: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/29.jpg)
Max Yield without Reserves
![Page 30: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/30.jpg)
Max Yield without Reserves
![Page 31: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/31.jpg)
Max Yield without Reserves
![Page 32: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/32.jpg)
Max Yield without Reserves
![Page 33: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/33.jpg)
Max Yield without Reserves
![Page 34: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/34.jpg)
Max Yield without Reserves
![Page 35: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/35.jpg)
A spectrum of high-profit scenariosMax Yield without Reserves
![Page 36: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/36.jpg)
A spectrum of high-profit scenarios
Cost = θ/density
Max Yield without Reserves
![Page 37: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/37.jpg)
A spectrum of high-profit scenarios
Cost = θ/density (Stop fishing when cost = $1)
Max Yield without Reserves
![Page 38: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/38.jpg)
A spectrum of high-profit scenarios
Cost = θ/density (Stop fishing when cost = $1)
Escapement = % of virgin K (K = 50)
Max Yield without Reserves
![Page 39: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/39.jpg)
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
![Page 40: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/40.jpg)
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
![Page 41: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/41.jpg)
A spectrum of high-profit scenariosθ/K = 15/50 = 30%
Max Yield without Reserves
![Page 42: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/42.jpg)
A spectrum of high-profit scenariosθ/K = 10/50 = 20%
Max Yield without Reserves
![Page 43: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/43.jpg)
A spectrum of high-profit scenariosθ/K = 5/50 = 10%
Max Yield without Reserves
![Page 44: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/44.jpg)
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.
![Page 45: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/45.jpg)
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)
![Page 46: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/46.jpg)
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
![Page 47: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/47.jpg)
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
![Page 48: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/48.jpg)
University of California – Santa Barbara
National Science Foundation
THANK YOU!
![Page 49: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/49.jpg)
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
![Page 50: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/50.jpg)
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
![Page 51: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/51.jpg)
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
![Page 52: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/52.jpg)
![Page 53: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/53.jpg)
![Page 54: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/54.jpg)
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
![Page 55: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/55.jpg)
![Page 56: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/56.jpg)
![Page 57: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/57.jpg)
![Page 58: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/58.jpg)
![Page 59: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/59.jpg)
Older, bigger fish produce many more young
![Page 60: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/60.jpg)
![Page 61: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/61.jpg)
Channel Islands
![Page 62: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/62.jpg)
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
![Page 63: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/63.jpg)
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
![Page 64: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/64.jpg)
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.
![Page 65: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/65.jpg)
![Page 66: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/66.jpg)
![Page 67: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/67.jpg)
Scale bar = 100 km
![Page 68: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/68.jpg)
Scale bar = 100 km
![Page 69: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/69.jpg)
Marine reserves and fishery profit: practical designs offer
optimal solutions.
Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara
![Page 70: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/70.jpg)
Can Marine Reserves bolster fishery
yields?
![Page 71: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/71.jpg)
NO RESERVES
RESERVES (E = 0% outside)
Larvae-on-larvae density dependence
equal
![Page 72: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/72.jpg)
![Page 73: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/73.jpg)
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.
![Page 74: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/74.jpg)
![Page 75: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/75.jpg)
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
![Page 76: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/76.jpg)
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
![Page 77: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/77.jpg)
![Page 78: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/78.jpg)
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
![Page 79: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/79.jpg)
![Page 80: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/80.jpg)
![Page 81: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/81.jpg)
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
![Page 82: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/82.jpg)
![Page 83: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/83.jpg)
![Page 84: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/84.jpg)
![Page 85: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/85.jpg)
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
![Page 86: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/86.jpg)
INCREASE
![Page 87: Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of.](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d4c5503460f94a2a54e/html5/thumbnails/87.jpg)
Costello and Ward. In Review.