Image source: Dr. James Bowen, UNC Charlotte

What can we learn from a lumped- parameter bioeconomic model about valuing ecosystem services?

Preview Develop a method that provides an exact welfare measure of a portion of ecosystem service value A 30% reduction in nitrogen loading in the Neuse generates $2.04 million in fisheries benefits under open access The value of the environmental change is contingent on the institutional arrangement

Outline Background and literature Analytical Model with Open Access Parameterizing the model (briefly) Qualitative and Quantitative Results Discussion of the results Linking Models of Economics and Ecosystems Preliminary results from a “quasi-optimized” model

The Problem Nitrogen in the estuary algae Oxygen demand hypoxia Migration into oxygenated areas (crowding) Prey Mortality

TMDL and the Neuse Nutrient pollution in Neuse linked to hypoxia/anoxia, toxic algal blooms, fish kills, effects on the trophic system Clean Water Act requires Total Maximum Daily Load (TMDL) plan Neuse TMDL recommends 30% reduction in nitrogen loadings Schwabe (2001) estimates annualized cost of 30% reduction ranges from $5.4 million to $9.1 million (1999 dollars) 9 species that depend on estuarine soft- bottom habitat make up > 2/3 dockside value of NC commercial fisheries (Peterson et al., 2000) Image Source: NCSU Center for Applied Aquatic Ecology pics-dp/dpncmap.gif Image Source:

NC Blue Crab Fishery Largest commercial fishery in NC ($34.4 million ex vessel revenues in 2002) 80,000 – 100,000 trips per year 35% in Neuse River and Pamlico Sound Essentially open access ~ 25 % of East Coast production from NC Image Source: Dept. of Fisheries Science, VIMS, William and Mary

Total Catch and Revenues

4 strands of the bioeconomic literature Multispecies models with predator-prey interaction (Hannesson, 1983; Ragozin and Brown, 1985; Kaplan and Smith, 2001; Brock and Xepapadeas, 2004) Habitat dependence of a renewable resource (Swallow, 1990; Barbier and Strand, 1998) Spatial fisheries models (Sanchirico and Wilen, 1999; Smith and Wilen, 2003) Empirical bioeconomics of open access (Wilen, 1976; Bjorndal and Conrad, 1987)

Model Structure Lumped-parameter system of 8 ordinary differential equations 1. Nutrient loadings accumulate in the estuary 2. Nutrient accumulation increases algal carrying capacity Two species 3. blue crabs as harvested mobile predator 4. clams as unharvested stationary prey Two patches 5. Patch 1 subject to hypoxia 6. Patch 2 has no hypoxia 7. Dynamic open access 8. Discrete choice model of fishing locations

Nutrients (N) and Algae (A) This parameter will matter a lot. Loadings minus natural decay Logistic growth a function of nutrients

Blue Crab (X) population dynamics Logistic growth predation harvest Hypoxia-induced migration Migration from relative prey availability

Blue Crab (X) population dynamics

Prey (Y) population dynamics Predation Logistic growth Hypoxia-induced mortality

Dynamic Open Access Rents are dissipated in the long run Transitional rents are the welfare metric Reducing hypoxia generates a short-run economic benefit by increasing prey stocks and reducing predator crowding

Dynamic Open Access Profit/Rent Function Vernon Smith Rent Dissipation  is speed of adjustment costs revenues Marginal cost of effort + opp cost of capital (per unit effort)

Spatial Effort Implied Dynamic Spatial Adjustment Adding up Define an effort share state variable Based on empirical fisheries economics literature

Closing the Model Schaefer Production q is “catchability”

Parameterization (Short Version) Nitrogen loadings, algal production, hypoxia, and prey mortality: Various pieces of the Neu-BERN model due to Borsuk, Stow, Reckhow, and others Blue Crab population dynamics: Eggleston et al. (2004) stock assessment and related work Blue crab migration: Eby and Crowder Costs – Rhodes, Lipton, and Shabman survey of Chesapeake blue crabbers Prices and trips– NC DMF data + BLS CPI South Size D Discount rate – 2.5% Other parameters – used nonlinear solver to back them out or used 1-period-ahead forecasting to choose them

Results Summary

No Reduction in Nitrogen – Initial Condition at ½ k x

Stretched cycles reflect sluggish adjustment

No Reduction in Nitrogen – Initial Condition at ½ k x

Time Path of Policy Impacts on Rents

Long dynamics troughs peaks

Time Path of Policy Impacts on Rents Stretching

Time Path of Policy Impacts on Rents Starts negative: initial effort level with more pollution closer to the optimal level

Time Path of Policy Impacts on Rents Most of gains in first 15 years

Time Path of Policy Impacts on Rents Bioeconomic Overshooting

Time Path of Policy Impacts on Rents Rent dissipation

Gains from reduced nutrient pollution could be much larger under a rationalized fishery

Time Path of Policy Impacts on Catch

Time Path of Policy Impacts on Effort

Sensitivity to Impact of Nitrogen on Primary Production

Sensitivity to Per Trip Costs

Sensitivity to Speed of Adjustment

Discussion PV cost of permanent 30% reduction (from Schwabe, 2000) using 2.5% discount rate $259.7 million (2002 dollars) Blue crab benefits are <1% of this cost Open access the culprit? Benefits to other fisheries Non-fishery benefits of ecosystem services

Linking Models in Economics and Ecology Direction of Effects Magnitude of Effects Timing of Effects Parameter Lumping

Direction of Effects Prey response to hypoxia Hypoxia-induced catchability increase Nutrients and hormesis

Magnitude of Effects Carrying capacities and the pristine system Patch 2 as “insurance”

Timing of Effects Hysteresis in oxygen demand –Nitrogen stocks –Algae stocks Intrinsic growth rates – how fast predators, prey, and algae “recover” Economic speed of adjustment (both timing and magnitude)

Parameter lumping Like a partial reduced-form –Use available information to put structure on the problem –Lumped parameters not directly measurable quantities in nature Example: Prey Death Parameter –Lumps algae-dissolved oxygen and dissolved oxygen-death together –Does not distinguish between “death” and growth retardation

How does ecosystem value depend on the management institution? Compare open access to optimal!

A “Quasi-Optimum” Grid Search over constant effort solutions –Search over total effort and share allocation to the patches Lower bound on total rents Difference in rents not necessarily bigger or smaller

Preliminary Results

Biological Dispersal and Effort Allocation A Marine Reserve in the “dirty” patch

Crab Indifference Two countervailing forces: –Crabs move away from hypoxic zones – increases relative prey availability –Hypoxia decreases absolute prey availability Crabs may respond to low oxygen at levels that are sub-lethal for prey Sink or source? A question for behavioral ecology

Preliminary Work on the Optimized Model

Other states do not feed back on nitrogen

Nomenclature H Current Value Hamiltonian  discount rate ccost of effort F 1 (X 1, X 2, Y 1, Y 2, A)Net Growth predator patch 1 F 2 (X 1, X 2, Y 1, Y 2, A)Net Growth predator patch 2 G 1 (X 1, X 2, Y 1, Y 2, A)Net Growth prey patch 1 G 2 (X 1, X 2, Y 1, Y 2, A)Net Growth prey patch 2  A, t)RHS of algae state equation Define Co-State Variables: 1 Predator 1 2 Predator 2 3 Prey 1 4 Prey 2 5 Algae

Current Value Hamiltonian

First Order Conditions

First Order Conditions (cont.) Two Switching Functions Plus all of the original state equations.

In Steady State 6 unknowns (E 1, E 2, X 1, X 2, Y 1, Y 2 ) and 6 equations

Additional Figures

Populations when Initial Conditions are 200-year States

30% Reduction in Nitrogen – Initial Condition at ½ k x