Harvesting stochastic, spatially connected fisheries Christopher Costello (UCSB) Stephen Polasky (UMN) F3 All-Hands-On July 12, 2006 Santa Barbara, CA

Fisheries are in decline Marine resources overexploited Marine resources overexploited 90% reduction in large predators (Myers & Worm) 90% reduction in large predators (Myers & Worm) Long history of over-exploitation in near-shore (Jackson et al.) Long history of over-exploitation in near-shore (Jackson et al.) Exploitation as the primary human disturbance of marine systems Exploitation as the primary human disturbance of marine systems Biological & Economic explanations, consequences Biological & Economic explanations, consequences

Addressing over-exploitation Economists: Economists: Institutional failure Institutional failure Solution is to regulate/privatize the commons Solution is to regulate/privatize the commons Example: individually transferable quotas (ITQs) Example: individually transferable quotas (ITQs) Biologists: Biologists: Over-exploitation (tragedy of commons, greed, or myopia) Over-exploitation (tragedy of commons, greed, or myopia) Recent solution: “Marine Protected Areas” Recent solution: “Marine Protected Areas” Recommendations for 30% of oceans to be closed Recommendations for 30% of oceans to be closed Good for the fish, good for the fishermen (Hastings & Botsford) Good for the fish, good for the fishermen (Hastings & Botsford)

Challenge to Economists Biological sciences have emphasized Biological sciences have emphasized Importance of spatial patterns Importance of spatial patterns Importance of variability and uncertainty Importance of variability and uncertainty Economics emphasizes incentives; but much of the existing work is a-spatial and deterministic (though there are notable exceptions) Economics emphasizes incentives; but much of the existing work is a-spatial and deterministic (though there are notable exceptions)

The world

Marine reserves in the world 11% of land, 1% of ocean is set aside in reserve

Worldwide area in reserves Reserves are being implemented at an increasing rate— Without guidance from economic analysis 2x size of Europe or Australia 20x size of Great Lakes

Rationale for reserves Two arguments are used for reserves Two arguments are used for reserves 1. Protect unexploited assemblages of species – biodiversity 2. Close an area, lose some harvest. But production increases in closed area. Larvae “spill-over” into exploited area. Could this increase overall harvest? Second claim is largely unsubstantiated. We will evaluate this claim. Second claim is largely unsubstantiated. We will evaluate this claim.

Inconsistent with economic intuition? “Unless we somewhat artificially introduce an intrinsic value for biomass in the sanctuary, there would be no rationale for a marine sanctuary in a deterministic world with perfect management” -J. Conrad (1999)

Biologists as policy makers Lack of data and formal analysis has not deterred biologists from giving policy advice: “It is time to trust the insights of ecologists for once, press for the establishment of marine reserves and place fisheries management and marine conservation on a sound basis at last.” -Roberts (1997)

Economists, on biologists “Owing to the lack of theoretical economic research, biologists have been forced to extend the scope of their own thought into the economic sphere and in some cases have penetrated quite deeply, despite the lack of the analytical tools of economic theory.” -- H. Scott Gordon (1954)

A thought experiment… What would a fisherman do if he “owned” the fishery? What would a fisherman do if he “owned” the fishery? Secure “right” for exclusive access Secure “right” for exclusive access Could harvest different amounts spatially Could harvest different amounts spatially Could account for dynamic and spatial externalities Could account for dynamic and spatial externalities Real-world institutions (e.g.): Real-world institutions (e.g.): Harvest cooperatives Harvest cooperatives TURFs TURFs Area-based quotas Area-based quotas

Spatial bioeconomics under uncertainty Spatial issues: Spatial issues: Most larvae disperse across space: 90% of near-shore marine harvested species have sessile adults, larval dispersal Most larvae disperse across space: 90% of near-shore marine harvested species have sessile adults, larval dispersal Economic payoffs may vary across space (e.g., costs of harvest) Economic payoffs may vary across space (e.g., costs of harvest) Spatial externalities exist when an action in one location affects other locations Spatial externalities exist when an action in one location affects other locations Stochasticity: Stochasticity: Environmental variability affects life-history stages, state transitions, impact of policy, and info about future Environmental variability affects life-history stages, state transitions, impact of policy, and info about future Dispersal itself may be variable Dispersal itself may be variable

Significance for policy Under a spatial/stochastic system, even making predictions is difficult – much less designing optimal spatial/temporal harvest Under a spatial/stochastic system, even making predictions is difficult – much less designing optimal spatial/temporal harvest How should policy be designed to manage spatial/stochastic resources? How should policy be designed to manage spatial/stochastic resources? Do harvest closures (MPAs) emerge as an economically optimal management instrument? Do harvest closures (MPAs) emerge as an economically optimal management instrument?

Research questions Optimal spatial harvest under uncertainty? Optimal spatial harvest under uncertainty? Role of spatial connections? Role of spatial connections? Permanent harvest closures ever optimal? How should they be designed? Permanent harvest closures ever optimal? How should they be designed? Temporary harvest closures ever optimal? Temporary harvest closures ever optimal? Optimal management outside a reserve? Optimal management outside a reserve?

Some of the relevant literature MPAs and fishery yield (Hastings & Botsford) MPAs and fishery yield (Hastings & Botsford) MPAs and open access or regulated open access outside (Sanchirico & Wilen) MPAs and open access or regulated open access outside (Sanchirico & Wilen) Spatial harvesting, no reserves (Sanchirico & Wilen) Spatial harvesting, no reserves (Sanchirico & Wilen) Optimal spatial harvesting in deterministic environment (Neubert, Clark) Optimal spatial harvesting in deterministic environment (Neubert, Clark) Game-theoretic spatial harvesting in deterministic environment (Bjorndal et al., Munro, Naito and Polasky) Game-theoretic spatial harvesting in deterministic environment (Bjorndal et al., Munro, Naito and Polasky) A-spatial optimal management under uncertainty (Reed, Costello et al.) A-spatial optimal management under uncertainty (Reed, Costello et al.)

Flow, Fish, and Fishing Flow – how are resources connected across space? [Resource Connectivity] Flow – how are resources connected across space? [Resource Connectivity] Fish – spatial heterogeneity of biological growth [Dynamic Externality and Spatial Heterogeneity] Fish – spatial heterogeneity of biological growth [Dynamic Externality and Spatial Heterogeneity] Fishing – harvesting incentives across space, economic objectives, distributional impacts over time [Economic Optimality] Fishing – harvesting incentives across space, economic objectives, distributional impacts over time [Economic Optimality]

“Patchy” dispersal vs. diffusion Simulation Result Diffusion Model This relationship is highly variable – not a smooth dispersal kernel We think of dispersal kernel as a probability distribution

A motivating example (2 patches) Current tends to flow towards B: Current tends to flow towards B: State equation in A: X t+1 =(1-  )F(X t -H t ) State equation in A: X t+1 =(1-  )F(X t -H t ) If profit is linear in harvest, want F’ =1/  in both patches If profit is linear in harvest, want F’ =1/  in both patches If we close A: If we close A: What is X ss ? What is rate of return? What is X ss ? What is rate of return? Is this > or or < 1/  ? A B  

x1Kx1K (1-  0 )F(x t ) F(x t ) x0Kx0K 45 o (1-  1 )F(x t ) xtxt x t+1 F’(x 0 K )<1/  F’(x 1 K )>1/  Dynamics in the closed patch (“A”) (low spillover) (high spillover) x*x* F’(x*)=1/ 

Generalizing the model Economics: Economics: Heterogeneous harvest cost, stock-effect on MC Heterogeneous harvest cost, stock-effect on MC Constant price Constant price Biology Biology Sessile adults Sessile adults Larval drift Larval drift Variability & Uncertainty Variability & Uncertainty Production and survival Production and survival Where larvae drift Where larvae drift

Timing Adult population in a location Settlement and survival to adulthood Larval production Spawning population (Escapement) Harvest Dispersal “D ij ” (Note here that harvest is location-specific)

Adding environmental variability Adult population in a location Settlement and survival to adulthood Larval production Spawning population (Escapement) Harvest zfzf Random dispersal “D ij ” zSzS zz (Note here that harvest is location-specific) shock to adult survival shocks to settlement and larval survival shock to fecundity

The marginal economic conditions p c(s) Biomass, s The cost of catching one more fish The benefit of catching one more fish The net benefit of catching one more fish xe Total profit from harvesting H fish (from initial population of x to an escapement of e) H MR, MC

Stochastic dynamic program Objective: Identify optimal feedback control rule (specifies harvest in each patch) to maximize expected present value from harvest over T periods Objective: Identify optimal feedback control rule (specifies harvest in each patch) to maximize expected present value from harvest over T periods State vector: current stock in every patch (x 1, …, x I ) State vector: current stock in every patch (x 1, …, x I ) Control vector: harvest (alternatively, escapement) in every patch (e 1, …, e I ) Control vector: harvest (alternatively, escapement) in every patch (e 1, …, e I ) In each time period t we have I state variables, and I control variables, t=1,….,T. In each time period t we have I state variables, and I control variables, t=1,….,T. Typically optimal escapement will be a function of the vector of current stocks: e it * (x 1t, …, x It ) for all i=1,…,I Typically optimal escapement will be a function of the vector of current stocks: e it * (x 1t, …, x It ) for all i=1,…,I

Problem setup Maximize E{NPV} of profits from harvest. Find optimal harvest strategy: Maximize E{NPV} of profits from harvest. Find optimal harvest strategy: Equation of motion: Equation of motion: Dynamic Programming Equation (vector notation): Dynamic Programming Equation (vector notation):

Solution procedure Discrete-time stochastic dynamic programming Discrete-time stochastic dynamic programming If an interior solution exists, this problem is state separable -- the necessary conditions are independent of the state vector If an interior solution exists, this problem is state separable -- the necessary conditions are independent of the state vector This makes finding a solution tractable This makes finding a solution tractable

Interior solution What is an interior solution? What is an interior solution? Optimal to have positive harvest in every patch in every time period Optimal to have positive harvest in every patch in every time period Proposition 1: If an interior solution to the DPE exists, optimal escapement will vary across space, but will be both time, and state independent Proposition 1: If an interior solution to the DPE exists, optimal escapement will vary across space, but will be both time, and state independent Constant patch-specific escapement level

Corner solutions: harvest closures (MPAs) Corner solution = harvest closure Corner solution = harvest closure Proposition 3: Patch i should be closed to harvesting in period t if and only if x it <e it *, where e it * satisfies equating marginal value of current harvest with expected marginal value of an additional unit of stock Proposition 3: Patch i should be closed to harvesting in period t if and only if x it <e it *, where e it * satisfies equating marginal value of current harvest with expected marginal value of an additional unit of stock If stock size in a patch is lower than a pre- determined escapement target, then it is optimal to close the patch

Harvest closures (MPAs) What bioeconomic conditions could lead to harvest closure? Three basic reasons: What bioeconomic conditions could lead to harvest closure? Three basic reasons: 1. Dispersal to a site is low relative to productivity of the site Ocean currents lead to poor dispersal to patch i Ocean currents lead to poor dispersal to patch i 2. High marginal harvest costs 3. “Bad” realizations of random variables lead to low recruitment in a patch 1&2 suggest permanent closure, 3 suggests temporary closure 1&2 suggest permanent closure, 3 suggests temporary closure Close patch to take advantage of high marginal productivity of site (relative to current returns) Close patch to take advantage of high marginal productivity of site (relative to current returns)

Optimal management outside optimally designed reserves Suppose a patch (k) is optimally closed, what to do outside that patch? Suppose a patch (k) is optimally closed, what to do outside that patch? Proposition 5: e it *(I kt+1 =0) 0) Proposition 5: e it *(I kt+1 =0) 0) Escape more fish outside (an optimally designed) reserve to take advantage of high marginal returns in the reserve

Optimal management outside sub- optimally designed reserves Suppose a patch is sub-optimally closed to harvest. What to do outside that patch? Suppose a patch is sub-optimally closed to harvest. What to do outside that patch? Proposition 6: Under A3 & A4, e it *(R kt+1 =1)<e it *(R kt+1 =0) Proposition 6: Under A3 & A4, e it *(R kt+1 =1)<e it *(R kt+1 =0) Escape fewer fish outside (a sub-optimally designed) reserve because of low marginal returns in the reserve

Summary 1. Constant “patch-specific escapement” (interior) 2. Reserves emerge as an optimal economic solution 3. Reserves can be optimal with & without stochastic environment 4. Optimal harvest outside reserves If reserves optimal – harvest outside decreases If reserves optimal – harvest outside decreases If reserves sub-optimal – harvest outside increases If reserves sub-optimal – harvest outside increases 5. Shortcomings include: known stock, constant price, harvest cost, no fully optimal corner sol’n.

Extensions to consider Institutions Institutions How big should cooperatives be? How big should cooperatives be? How should TURFs be defined? How should TURFs be defined? How to solve the coordination problem? How to solve the coordination problem? E.g. pay one guy not to fish through self-taxation E.g. pay one guy not to fish through self-taxation How hard is this framework to implement with real data? [tomorrow] How hard is this framework to implement with real data? [tomorrow]