Economics, Density Dependence and the Efficacy of Marine Reserves Crow White Ph.D. Chapter.

Economics, Density Dependence and the Efficacy of Marine Reserves

Crow White

Ph.D. Chapter

Spatially and Temporally Explicit Integrodifference Model

Settlers at x =

R = proportion of settlers that successfully recruit into the local population

For coastal fish species:

Myers & Cadigan 1993

Botsford & Hobbs 1995

Carr et al. 1995

Caley et al. 1996

Fokvord 1997

Hixon & Webster 2002

Webster 2003

Skajaa et al. In Prep.

Cod

Dungeness & rock crabs

Rockfish

http://www.larvalbase.org/

Even when fishing is expensive reserves can enhance fishery profit

Equivalence

White et al. 2008 Ecology LettersWhite et al. 2008 Ecology Letters

Cohort of juvenile chromis (Baja California, Mexico)

Settler

Settler

Non-fishery species:

Gobies, damselfish and other small reef fish (Forrester, Steele, Osenberg and Schmitt/Holbrook laboratories)

Settler

Fishery species:

Kelp bass (White and Caselle 2008)

Rockfish (Johnson 2006)

Non-fishery species:

Gobies, damselfish and other small reef fish (Forrester, Steele, Osenberg and Schmitt/Holbrook laboratories)

POPULATION REGULATION

Density dependent larval recruitment

Inter-cohort: Adults compete with larvae for space and food, as well as eat them.

Intra-cohort: Larvae compete amongst themselves for space and food.

Across the recruitment period:

Larva settles

time →

Mature, legal-to-fish adult


Larva settles


time →

Inter-cohort density dependence

Intra-cohort density dependence

1. Simultaneous inter- and intra-cohort density dependence

- Adults and settlers interact across entire recruitment period

- Settlers compete amongst themselves for resources (food, shelter) across the entire recruitment period


Larva settles

time →



2. Sequential: inter-cohort then intra-cohort density dependence

- Adults only affect mortality early in recruitment period (e.g. when settlers are small and most vulnerable to predation)

- Settlers only compete for resources later in recruitment period (e.g. when they are sub-adults and have larger resource

requirements)



Larva settles

time →



2. Sequential: intra-cohort then inter-cohort density dependence

- Larvae settle to micro-habitat (shallow water zones, kelp forest canopy) different than where adults reside, thus delaying inter-cohort interactions.


Simultaneous inter- and intra-cohort density dependence

Inter-cohort Intra-cohort

S = # settlers

N = #adults (constant)

a & b = coefficients

(Verhurlst 1838)


S = # settlers



R = proportion settlers that recruit

So = #initial settlers

Alpha = a*t

Beta = b/a = relative strength of the two density dependent processes [0-infinity]



S = # settlers





Alpha = a*t


Given Beta = b = 0 (i.e. 100% inter-cohort DD)



S = # settlers





Alpha = a*t


Given Beta = b = 0 (i.e. 100% inter-cohort DD): Ricker formulation



S = # settlers





Alpha = a*t


Given a = 0 (i.e. 100% intra-cohort DD)



S = # settlers





Alpha = a*t


Given a = 0 (i.e. 100% intra-cohort DD)



S = #settlers





Alpha = a*t


Gamma = b*t

Given a = 0 (i.e. 100% intra-cohort DD): Beverton-Holt formulation


Functional representations of density dependent processes

Inter-cohort: Ricker. Over-compensatory due to additive effects of competition and (possibly aggregative) predation.

Intra-cohort: Beverton-Holt. Compensatory due to contest-competition for food and refugia.

Sequential: intra- then inter-cohort density dependence

g = overall strength of density dependence

D = relative strength of two density dependent processes

D = 0 100% inter-cohort

D = 1 100% intra-cohort

Intra-cohort (Beverton-Holt) Inter-cohort (Ricker)

Sequential: intra- then inter-cohort density dependence





Sequential: inter- then intra-cohort density dependence





Inter-cohort (Ricker)

Intra-cohort (Beverton-Holt)

# Settlers left after inter-cohort density dependent mortality

Sequential: inter- then intra-cohort density dependence





Relative strengths of inter- versus intra-cohort density dependence

Value when…

Model Parameter 100% inter-cohort 100% intra-cohort

Sequential D 0 1

Simultaneous Beta 0 Infinity


Value when…


Sequential D 0 1


Transformation

D = Beta / (1 + Beta)

Beta = D / (1 – D)


Value when…


Sequential D 0 1


Transformation

D = Beta / (1 + Beta)

Beta = D / (1 – D)Demographic density dependence independent variable

FISHING COSTS MONEY…

Cost of catching a fish increases as you harvest down the population

PROFIT =

Pre-harvest

Fishery yield at location x during time

step t

Revenue

Post-harvest

PROFIT =

Pre-harvest

Fishery yield at location x during time

step t

Revenue - Cost

Post-harvest integrate

Marginal cost = Fish density

θ

θ = 10

Stock Effect (Clark 1990)


θ



θ

Economic density dependence independent variable

Given the relative strength of inter- versus intra-cohort density dependent recruitment (D) and

the intrinsic cost-of-harvest of the fishery species (θ) can reserves increase fishery profit?

Parameter/variable Values evaluated Description

Aeq[H = 0] 100 Equilibrium virgin population density (fish per km), where H = harvest

M 0.05, 0.1, 0.2, 0.3 Natural adult mortality probability

P 1, 2, 3 Adult per capita production of larvae that survive to settlement

α, γ, g Solved for R = M/P, given H = 0

Density dependent recruitment coefficient, where R = proportion settlers that recruit

Dd 10, 100, 200 Mean larval dispersal distance (km) for calculating Kx-x’. Only one value (100 km)

was simulated (see Methods)

p 1 Price ($ per fish) = marginal revenue

θ 0, 1, 2… 20 Stock effect coefficient ($ * km-1)

D 0, 0.05, 0.1… 1 Inter- versus intra-cohort density dependent recruitment scaling parameter

(Ax – Hx)/(Aeq[H = 0]) 0.01, 0.02, 0.03…0.9 Escapement

Frac(x[Hx = 0]) 0, 0.05, 0.1… 0.75 Proportion coast in reserves

7,064,820 Total number of scenarios simulated

Inter-cohort

Intra-cohort

Hastings and Botsford 1999

White et al. 2008Gaylord et al. 2006, White & Kendall 2007

Inter-cohort

Intra-cohort

Inter-cohort

Intra-cohort

Inter-cohort

Intra-cohort

Demographic density dependence

Simultaneous inter-cohort 1st intra-cohort 1st

What is this model missing?

Factor [Effect on profit with reserves]

Age/stage structure (BOFFs) + (Gaylord et al. 2005)

Environmental stochasticity or management uncertainty

+ (Armsworth & Roughgarden 2003, Stefansson & Rosenberg 2005, 2006, Costello and Polasky In Press)

Heterogeneity in habitat conditions or fishing pressure

+ (Sanchirico et al. 2006, Ralston & O’Farrell 2008)

Adult movement (spill-over) ~, + when compared with over-exploited (Kellner et al. 2007)



GENERAL MESSAGE: OPTIMISTIC, PESSIMISTIC OR “IT DEPENDS”??

Inter-cohort

Intra-cohort

Policy: P6 = A priori constant % MPA and flexible escapement













GENERAL MESSAGE: OPTIMISTIC, PESSIMISTIC OR “IT DEPENDS”??

Inter-cohort

Intra-cohort


0 D 1

100% inter-cohort

100% intra-

cohort

Good Reserves? Bad


Linking D-values to species (some ideas):

0 D 1

100% inter-cohort

100% intra-

cohort

Good Reserves? Bad


0 D 1

100% inter-cohort

100% intra-

cohort

Good Reserves? Bad


1. Non-predatory, bottom-dwellers (e.g. urchins, abalone)

- Adults only affect settlers via competition

- Reduced inter-cohort density dependence

- Resource habitat reduced to 2-dimensions (horizontal)

- Enhanced intra-cohort density dependence



2. Cannibalistic (e.g. cod, kelp bass, rock crabs)

- Enhanced inter-cohort predation

0 D 1

100% inter-cohort

100% intra-

cohort

Good Reserves? Bad




2. Cannibalistic (e.g. cod, kelp bass, rock crabs)

- Enhanced inter-cohort predation

- Also adults are territorial (rockfish?)

- Enhanced inter-cohort competition

0 D 1

100% inter-cohort

100% intra-

cohort

Good Reserves? Bad


Cost of fishing

0 Theta 20

Harvest with perfect efficiency

Harvests costs

exorbitant

Good Reserves? Bad

Linking Theta-values to fisheries (some ideas):

Cost of fishing

0 Theta 20


Harvests costs

exorbitant

Good Reserves? Bad

time


1. Technology can improve harvesting efficiency

Cost of fishing

0 Theta 20


Harvests costs

exorbitant

Good Reserves? Bad

time



2. Personnel-intensive fishery (urchin diving) costly

- But what about price?

Cost of fishing



2. Personnel-intensive fishery (urchin diving) costly

- But what about price?

3. Open-access (“race to fish”) fisheries filled to over-capacity are inefficient

4. Limited-entry, dedicated access fisheries (with ITQs, TURFs) are efficient

0 Theta 20


Harvests costs

exorbitant

Good Reserves? Bad

time

Open-access

ITQs, TURFs

Are reserves good or bad??

1. Good for dedicated-access fisheries targeting predatory species

2. Bad for open-access fisheries targeting benthic grazers

3. Will get better over time as harvesting efficiency improves

4. In general, better than this study indicates due to simplifying assumptions of the model

FISHERY PROFIT UNDER OPTIMAL RESERVE VS. CONVENTIONAL MANAGEMENT

Ricker P = 1 m = 0.1

FISHERY PROFIT UNDER OPTIMAL RESERVE VS. CONVENTIONAL MANAGEMENT

Hastings & Botsford 1999

Gaylord et al. 2005 White & Kendall 2007

Costello & Ward In Prep.

White et al. In Review

Density Dependent Marginal Cost of Harvest

Density Dependent Marginal Cost of Harvest

Resolution of analysis

Proportion coast in reserves: 5%

Escapement level: 1%



θ

θ = 10

Modeling both inter- and intra-cohort density dependence

Across the recruitment period (age at settlement to age when mature, legal-to-fish adult)…










- Adults only affect mortality early in recruitment period (e.g. when settlers are small and most vulnerable to predation); and/or settlers only compete for resources later in recruitment period (e.g. when they are sub-adults and have larger resource requirements)






- Adults only affect mortality early in recruitment period (e.g. when settlers are small and most vulnerable to predation); and/or settlers only compete for resources later in recruitment period (e.g. when they are sub-adults and have larger resource requirements)

3. Sequential: intra-cohort then inter-cohort density dependence

- Larvae settle to micro-habitat (shallow water zones, kelp forest canopy) different than where adults reside, thus delaying inter-cohort interactions.

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Economics, Density Dependence and the Efficacy of Marine Reserves Crow White Ph.D. Chapter.

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