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 Caley et al Fokvord 1997 Hixon & Webster 2002 Webster 2003 Skajaa et al. In Prep. Cod Dungeness & rock crabs Rockfish

Even when fishing is expensive reserves can enhance fishery profit Equivalence White et al Ecology Letters

Cohort of juvenile chromis (Baja California, Mexico)

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

Across the recruitment period: Larva settles Mature, legal-to-fish adult 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

Across the recruitment period: Larva settles time → Inter-cohort density dependence Intra-cohort density dependence 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) Mature, legal-to-fish adult

Across the recruitment period: Larva settles time → Inter-cohort density dependence Intra-cohort density dependence 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. Mature, legal-to-fish adult

Simultaneous inter- and intra-cohort density dependence Inter-cohort Intra-cohort S = # settlers N = #adults (constant) a & b = coefficients (Verhurlst 1838)

Inter-cohort Intra-cohort S = # settlers N = #adults (constant) a & b = coefficients R = proportion settlers that recruit So = #initial settlers Alpha = a*t Beta = b/a = relative strength of the two density dependent processes [0-infinity] Simultaneous inter- and intra-cohort density dependence

Inter-cohort Intra-cohort S = # settlers N = #adults (constant) a & b = coefficients R = proportion settlers that recruit So = #initial settlers Alpha = a*t Beta = b/a = relative strength of the two density dependent processes [0-infinity] Given Beta = b = 0 (i.e. 100% inter-cohort DD) Simultaneous inter- and intra-cohort density dependence

Inter-cohort Intra-cohort S = # settlers N = #adults (constant) a & b = coefficients R = proportion settlers that recruit So = #initial settlers Alpha = a*t Beta = b/a = relative strength of the two density dependent processes [0-infinity] Given Beta = b = 0 (i.e. 100% inter-cohort DD): Ricker formulation Simultaneous inter- and intra-cohort density dependence

Inter-cohort Intra-cohort S = # settlers N = #adults (constant) a & b = coefficients R = proportion settlers that recruit So = #initial settlers Alpha = a*t Beta = b/a = relative strength of the two density dependent processes [0-infinity] Given a = 0 (i.e. 100% intra-cohort DD) Simultaneous inter- and intra-cohort density dependence

Inter-cohort Intra-cohort S = # settlers N = #adults (constant) a & b = coefficients R = proportion settlers that recruit So = #initial settlers Alpha = a*t Beta = b/a = relative strength of the two density dependent processes [0-infinity] Given a = 0 (i.e. 100% intra-cohort DD) Simultaneous inter- and intra-cohort density dependence

Inter-cohort Intra-cohort S = #settlers N = #adults (constant) a & b = coefficients R = proportion settlers that recruit So = #initial settlers Alpha = a*t Beta = b/a = relative strength of the two density dependent processes [0-infinity] Gamma = b*t Given a = 0 (i.e. 100% intra-cohort DD): Beverton-Holt formulation Simultaneous inter- and intra-cohort density dependence

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 = 1100% intra-cohort Intra-cohort (Beverton-Holt) Inter-cohort (Ricker)

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 = 1100% intra-cohort

Sequential: inter- then intra-cohort density dependence g = overall strength of density dependence D = relative strength of two density dependent processes D = 0 100% inter-cohort D = 1100% intra-cohort Inter-cohort (Ricker) Intra-cohort (Beverton-Holt) # Settlers left after inter-cohort density dependent mortality

Sequential: inter- then intra-cohort density dependence g = overall strength of density dependence D = relative strength of two density dependent processes D = 0 100% inter-cohort D = 1100% intra-cohort

Relative strengths of inter- versus intra-cohort density dependence Value when… ModelParameter100% inter-cohort100% intra-cohort SequentialD01 SimultaneousBeta0Infinity

Relative strengths of inter- versus intra-cohort density dependence Value when… ModelParameter100% inter-cohort100% intra-cohort SequentialD01 SimultaneousBeta0Infinity Transformation D = Beta / (1 + Beta) Beta = D / (1 – D)

Relative strengths of inter- versus intra-cohort density dependence Value when… ModelParameter100% inter-cohort100% intra-cohort SequentialD01 SimultaneousBeta0Infinity 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)

Marginal cost = Fish density θ Stock Effect (Clark 1990)

Marginal cost = Fish density 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/variableValues evaluatedDescription A eq [H = 0]100Equilibrium virgin population density (fish per km), where H = harvest M0.05, 0.1, 0.2, 0.3Natural adult mortality probability P1, 2, 3Adult per capita production of larvae that survive to settlement α, γ, gSolved for R = M/P, given H = 0 Density dependent recruitment coefficient, where R = proportion settlers that recruit DdDd 10, 100, 200Mean larval dispersal distance (km) for calculating K x-x’. Only one value (100 km) was simulated (see Methods) p1Price ($ per fish) = marginal revenue θ0, 1, 2… 20Stock effect coefficient ($ * km -1 ) D0, 0.05, 0.1… 1Inter- versus intra-cohort density dependent recruitment scaling parameter (A x – H x )/(A eq [H = 0])0.01, 0.02, 0.03…0.9Escapement Frac(x[H x = 0])0, 0.05, 0.1… 0.75Proportion coast in reserves 7,064,820Total number of scenarios simulated

Inter-cohort Intra-cohort

Hastings and Botsford 1999 White et al Gaylord et al. 2006, White & Kendall 2007 Inter-cohort Intra-cohort

Inter-cohort Intra-cohort

Inter-cohort Intra-cohort

Demographic density dependence Simultaneous inter-cohort 1 st intra-cohort 1 st

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)

Hastings and Botsford 1999 White et al Gaylord et al. 2006, White & Kendall 2007 GENERAL MESSAGE: OPTIMISTIC, PESSIMISTIC OR “IT DEPENDS”?? Inter-cohort Intra-cohort

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

Hastings and Botsford 1999 White et al Gaylord et al. 2006, White & Kendall 2007 GENERAL MESSAGE: OPTIMISTIC, PESSIMISTIC OR “IT DEPENDS”?? Inter-cohort Intra-cohort

Relative strengths of inter- versus intra-cohort density dependence 0D10D1 100% inter- cohort 100% intra- cohort Good Reserves? Bad

Relative strengths of inter- versus intra-cohort density dependence Linking D-values to species (some ideas): 0D10D1 100% inter- cohort 100% intra- cohort Good Reserves? Bad

Relative strengths of inter- versus intra-cohort density dependence 0D10D1 100% inter- cohort 100% intra- cohort Good Reserves? Bad Linking D-values to species (some ideas): 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

Relative strengths of inter- versus intra-cohort density dependence Linking D-values to species (some ideas): 2. Cannibalistic (e.g. cod, kelp bass, rock crabs) - Enhanced inter-cohort predation 0D10D1 100% inter- cohort 100% intra- cohort Good Reserves? Bad

Relative strengths of inter- versus intra-cohort density dependence Linking D-values to species (some ideas): 2. Cannibalistic (e.g. cod, kelp bass, rock crabs) - Enhanced inter-cohort predation - Also adults are territorial (rockfish?) - Enhanced inter-cohort competition 0D10D1 100% inter- cohort 100% intra- cohort Good Reserves? Bad

Cost of fishing 0Theta20 Harvest with perfect efficiency Harvests costs exorbitant Good Reserves? Bad Linking Theta-values to fisheries (some ideas):

Cost of fishing 0Theta20 Harvest with perfect efficiency Harvests costs exorbitant Good Reserves? Bad time Linking Theta-values to fisheries (some ideas): 1. Technology can improve harvesting efficiency

Cost of fishing 0Theta20 Harvest with perfect efficiency Harvests costs exorbitant Good Reserves? Bad time Linking Theta-values to fisheries (some ideas): 1. Technology can improve harvesting efficiency 2. Personnel-intensive fishery (urchin diving) costly - But what about price?

Cost of fishing Linking Theta-values to fisheries (some ideas): 1. Technology can improve harvesting efficiency 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 0Theta20 Harvest with perfect efficiency 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 White & Kendall 2007 Costello & Ward In Prep. White et al. In Review

Density Dependent Marginal Cost of Harvest

 Resolution of analysis  Proportion coast in reserves: 5%  Escapement level: 1%

Stock Effect (Clark 1990) Marginal cost = Fish density 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)…

Modeling both inter- and intra-cohort density dependence Across the recruitment period (age at settlement to age when mature, legal-to-fish adult)… 1. Simultaneous inter- and intra-cohort density dependence - Adults and settlers interact across entire recruitment period

Modeling both inter- and intra-cohort density dependence Across the recruitment period (age at settlement to age when mature, legal-to-fish adult)… 1. Simultaneous inter- and intra-cohort density dependence - Adults and settlers interact across entire recruitment period 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); and/or settlers only compete for resources later in recruitment period (e.g. when they are sub-adults and have larger resource requirements)

Modeling both inter- and intra-cohort density dependence Across the recruitment period (age at settlement to age when mature, legal-to-fish adult)… 1. Simultaneous inter- and intra-cohort density dependence - Adults and settlers interact across entire recruitment period 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); 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.