Optimal monitoring and control under state uncertainty: Application to lionfish management

State variables in many renewable resource management problems, such as the abundance of a fish stock, are imperfectly observed over time. In systems characterized by state uncertainty, decision makers often invest in monitoring to learn about the level of a stock. We develop a stochastic bioeconomic model of marine invasive species management under state uncertainty. The decision maker in our model simultaneously evaluates optimal investment in monitoring and population control. Using a recently-devised method for solving continuous-state Partially Observable Markov Decision Processes (POMDPs), we find that the ability to learn through monitoring can alter the role of population control in the optimal policy function, for example by reducing control intensity in favor of monitoring. Optimal monitoring depends on the management context, including in our application lionfish population structure. The rich transient dynamics of our model depend critically on the relationship between the initial conditions for information and invader abundance.     

Legalizing markets and the consequences for poaching of wildlife species: the vicuña as a case study

Vicuña provide an excellent case study for examining the sustainable use of wildlife outside protected areas: the community-based conservation approach. Vicuña populations in the high Andes of Argentina, Bolivia, Chile, Ecuador and Perú fell to a critically low level, but a Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) ban on trade in their fiber has seen numbers recover dramatically, and now live shearing of vicuña for a high-value international market is being promoted as a mechanism to secure both sustainable vicuña populations and local livelihoods. We used a dynamic optimization model to explore the consequences of legalizing markets, including the consequences for poaching which is critical in vicuña dynamics. Using parameters obtained from the literature and expert knowledge, we explored different scenarios for the Argentine region of Cieneguillas. Our results showed that the role of the international market is ambiguous; live shearing for an international market can provide the very best of outcomes for both vicuña and local people, with large herds generating high revenues. But an international market also creates a market for poached vicuña fiber; as a result, vicuña numbers risk once again falling to critically low levels, resulting also in minimal revenues from sale of fiber. The message for the international community is that if community-based conservation is not implemented carefully then its impact can easily be perverse.     

No sympathy for the devil

Pathogens are a significant driver of biodiversity loss. We examine two wildlife disease management strategies that have seen growing use, sometimes in combination: (i) trapping-and-culling infectious animals (disease control), and (ii) trapping-and-translocating healthy animals to a reserve, with possible future reintroduction. A reserve can improve conservation when there is no disease. But, when infection exists, we show investing in the reserve may counteract disease control. We find jointly pursuing both strategies is sub-optimal when the reserve is costly to maintain. Numerically, we examine management of Devil Facial Tumor Disease, which has generated extinction risks for Tasmanian Devils. Disease control (though not eradication) is generally part of an optimal strategy, although a reserve is also optimal if it can be maintained costlessly. This implies preserving the original population by addressing in situ conservation risks, rather than translocating animals to a reserve and giving up on the original population, is generally the first-best.     

Solving multidimensional bioeconomic problems with singular-perturbation reduction methods: Application to managing pest resistance to pesticidal crops

We investigate the application of ‘singular-perturbation’ reduction methods from the dynamical-systems literature to solve continuous-time multidimensional bioeconomic models resulting from integrating economics with increasingly complex biological structures. These methods reduce multidimensional solution space to the lower-dimensional subspace confining long-term dynamics. They arise naturally in problems with state variables evolving on widely disparate time scales. In particular, we demonstrate how the methods reduce the solution space of a linear-control specification—characterized by two state variables adjusting at widely disparate rates—to a single differential equation in the slow variable. All other system variables are determined by algebraic equations. We apply singular-perturbation methods to investigate the optimal management of pest resistance to pesticidal crops. The pest population evolves on a fast-time scale, while the population's genetic composition evolves on a slow-time scale. In comparison with past work, we can more fully characterize the continuous-time dynamics associated with a complex genetic specification.     

Econometric modeling of fisheries with complex life histories: Avoiding biological management failures

Economics of the fishery has focused on the wastefulness of common pool resource exploitation. Pure open access fisheries dissipate economic rents and degrade biological stocks. Biologically managed fisheries also dissipate rents but are thought to hold biological stocks at desired levels. We develop and estimate an empirical bioeconomic model of the Gulf of Mexico gag fishery that questions the presumptive success of biological management. Unlike previous bioeconomic life history studies, we provide a way to circumvent calibration problems by embedding our estimation routine directly in the dynamic bioeconomic model. We nest a standard biological management model that accounts for complex life history characteristics of the gag. Biological intuition suggests that a spawning season closure will reduce fishing pressure and increase stocks, and simulations of the biological management model confirm this finding. However, simulations of the empirical bioeconomic model suggest that these intended outcomes of the spawning closure do not materialize. The behavioral response to the closure appears to be so pronounced that it offsets the restriction in allowable fishing days. Our results indicate that failure to account for fishing behavior may play an important role in fishery management failures.     

Valuation of natural capital under uncertain substitutability

Natural capital is complex to value notably because of the high uncertainties surrounding the substitutability of its future ecosystem services. We examine a Lucas economy in which a consumption good is produced by combining different inputs, one of them being an ecosystem service that is partially substitutable with other inputs. The growth rate of these inputs and the elasticity of substitution evolve in a stochastic way. We characterize the socially efficient ecological discount rates that should be used to value future ecosystem services at different time horizons. We show that the inverse of the elasticity of substitution can be interpreted as the CCAPM beta of natural capital. We also show that any increase in risk of this beta reduces the ecological discount rate. If our collective beliefs about the elasticity of substitution of ecosystem services are Gaussian, the ecological discount rates go to minus infinity for finite maturities. In that case, a marginal increase in natural capital has an infinite value. We provide a realistic calibration of the model that is coherent with observed asset prices by using the model of extreme events of Barro (2006). The bliss maturity for infinite discount factors is less than 100 years in this calibration.     

Economics of harvesting age-structured fish populations

A generic age-structured model is developed to derive analytical results on optimal harvesting. Given two age classes, knife-edge selectivity, and no stock-dependent harvesting cost, the steady state is a unique saddle point. Adding harvesting cost does not alter the uniqueness, given that the utility is linear. Under specific conditions such as nonselective gear, optimal harvesting is proved to be a stationary cycle that represents pulse fishing. Optimal steady states are different if age-structured information is ignored and optimization is based on traditional biomass variables. This implies that the existence of optimal sustainable harvesting depends on age-structured information. Given a specific set of conditions such as low interest rate and knife-edge selectivity, optimal harvesting converges toward a unique saddle point independently of the number of age classes.