Optimal harvesting of ecologically interdependent fish species

The optimal exploitation of a two-species predator-prey system is considered, using Lotka-Volterra-type equations. Due to the density-dependence of ecological efficiency, both species should be harvested simultaneously over a range of relative prices. Beyond the limits of this price range, either the prey species should be utilized indirectly by harvesting the predator, or the predator should be eliminated to maximize the prey yield. Neglecting harvesting costs, the simultaneous harvest of prey and predators requires that a unit of prey biomass increase in value by being “processed” by predators. Certain results from single-species fishery models are shown not to apply to multispecies models. These are as follows: (i) Optimal regulation of a free access fishery may call for subsidizing instead of taxing the harvest of predator species. (ii) Increasing the discount rate may, at “moderate” levels, imply that the optimal standing stock of biomass increases instead of decreasing. (iii) A rising price or a falling cost per unit fishing effort of a species may raise and not lower the optimal standing stock of that species.     

Seasonal density dependence, timing of mortality, and sustainable harvesting

Birth-pulse populations are often characterized with discrete-time models, that use a single function to relate the post-breeding population size to the post-breeding size of the previous year. Recently, models of seasonal density dependence have been constructed that emphasize interactions during shorter time periods also. Here, we study two very simple forms of density-dependent mortality, that lead to Ricker and Beverton-Holt type population dynamics when viewed over the whole year. We explore the consequences of harvest timing to equilibrium population sizes under such density dependence. Whether or not individual mortality compensates for the harvested quota, the timing of harvesting has a strong impact on the sustainability of a harvesting quota. Further, we show that careless discretization of a continuous mortality scheme may seriously underestimate the reduction in population size caused by hunting and overestimate the sustainable yield. We also introduce the concept of the demographic value of an individual, which reflects the expected contribution to population size over time in the presence of density dependence. Finally, we discuss the possibility of calculating demographic values as means of optimizing harvest strategies. Here, a Pareto optimal harvest strategy will minimize the loss of demographic value from the population for a given yield.     

The optimal time path of clean energy R&D policy when patents have finite lifetime

We study the optimal time path for clean energy innovation policy. In a model with emission reduction through clean energy deployment, and with R&D increasing the overall productivity of clean energy, we describe optimal R&D policies jointly with emission pricing policies. We find that while emission prices can be set at the Pigouvian level independently of innovation policy, the optimal level of R&D subsidies and patent lifetime change with the stages of the climate problem. In the early stages of clean energy development, innovators find it more difficult to capture the social value of their innovations. Thus, for a given finite patent lifetime, optimal clean energy R&D subsidies are initially high, but then fall over time. Alternatively, if research subsidies are kept constant, the optimal patent lifetime should initially be long and fall over time.     

Optimal harvesting of a plant-hervibore system: lichen and reindeer in northern Finland

The optimal harvesting policy for a plant-herbivore system consisting of lichen and reindeer in Finnish Lapland is investigated. Using a discrete time model with no age structure it is shown that the optimal procedure to reach target levels for lichen and reindeer involves a possible initial harvest of reindeer and then a sequence of no-harvesting years until the lichen has recovered. After two adjusting harvests the system will settle to an equilibrium. The optimal solution is compared with the fastest possible approach to the target levels. The two solutions coincide if future yields are sufficiently discounted. With a discount factor near one there will be a heavier initial harvest in the optimal solution. It is seen that allowing some harvesting also in the no-harvesting years has no marked effect on the total yield. The target levels for lichen and reindeer are not unique but depend both on discounting and on the length of the planning period.     

Optimal control of Atlantic population Canada geese

Management of Canada geese (Branta canadensis) can be a balance between providing sustained harvest opportunity while not allowing populations to become overabundant and cause damage. In this paper, we focus on the Atlantic population of Canada geese and use stochastic dynamic programming to determine the optimal harvest strategy over a range of plausible models for population dynamics. There is evidence to suggest that the population exhibits significant age structure, and it is possible to reconstruct age structure from surveys. Consequently the harvest strategy is a function of the age composition, as well as the abundance, of the population. The objective is to maximize harvest while maintaining the number of breeding adults in the population between specified upper and lower limits. In addition, the total harvest capacity is limited and there is uncertainty about the strength of density-dependence. We find that under a density-independent model, harvest is maximized by maintaining the breeding population at the highest acceptable abundance. However if harvest capacity is limited, then the optimal long-term breeding population size is lower than the highest acceptable level, to reduce the risk of the population growing to an unacceptably large size. Under the proposed density-dependent model, harvest is maximized by maintaining the breeding population at an intermediate level between the bounds on acceptable population size; limits to harvest capacity have little effect on the optimal long-term population size. It is clear that the strength of density-dependence and constraints on harvest significantly affect the optimal harvest strategy for this population. Model discrimination might be achieved in the long term, while continuing to meet management goals, by adopting an adaptive management strategy.     

Harvest policies and nonmarket valuation in a predator — prey system

Although prey may not have commercial value, their economic value can be ascertained in a predator-prey model if the predator has a harvest value. The economic optimal (recovery) path of the predator and prey are carefully described when growth is quadratic in the predator (prey) and linear in prey (predator). Parameter values, in part, resembling Pacific halibut are used to provide numerical illustrations.     

Externalities, Market Power, and Resource Extraction

This article analyzes the effect of market power in the presence of dynamic and biological externalities. When several countries harvest fish in international waters the evolution of fish population is affected by their joint action, thus generating a biological and a dynamic externality. If there is trade, the market-clearing prices depend on the harvesting and consumption in all countries. Therefore, market-clearing prices also generate an externality. We find a subgame perfect Cournot–Nash equilibrium and study the conditions under which it may be efficient. We also analyze the role of different externalities in generating inefficiency.     

The development of secondary industries through the sustainable utilisation of reeds and forest timber in the Tembe Elephant Park,Maputaland, South Africa

The harvesting of Phragmites australis reeds in the Tembe Elephant Park has to be managed pro-actively. Solutions to potential problems should be sought before they arise. This paper offers a potential solution to the problem of instating a winter-only reed harvest in the Muzi Swamp. The potential for manufacturing finished products such as prefabricated huts from sustainably harvested reeds and forest timber is examined and a cost estimate is presented. A prefabricated reed hut is three-times cheaper than a similarly-sized house made of bricks and cement. The manufacturing of finished products from the harvested material will add secondary value to the resource and also offer an alternative employment to harvesting reeds in the summer. The higher prices obtained for a processed article will also, hopefully, reduce the demand for the resource in its raw form, thereby increasing the perceived value of the resource and reducing wastage from raw materials that are not sold.     

The Influence of Model Structure on Conclusions about the Viability and Harvesting of Serengeti Wildebeest

We investigate how the viability and harvestability predicted by population models are affected by details of model construction. Based on this analysis we discuss some of the pitfalls associated with the use of classical statistical techniques for resolving the uncertainties associated with modeling population dynamics. The management of the Serengeti wildebeest (Connochaetes taurinus) is used as a case study. We fitted a collection of age-structured and unstructured models to a common set of available data and compared model predictions in terms of wildebeest viability and harvest. Models that depicted demographic processes in strikingly different ways fitted the data equally well. However, upon further analysis it became clear that models that fit the data equally well could nonetheless have very different management implications. In general, model structure had a much larger effect on viability analysis (e.g., time to collapse) than on optimal harvest analysis (e.g., harvest rate that maximizes harvest). Some modeling decisions, such as including age-dependent fertility rates, did not affect management predictions, but others had a strong effect (e.g., choice of model structure). Because several suitable models of comparable complexity fitted the data equally well, traditional model selection methods based on the parsimony principle were not practical for judging the value of alternative models. Our results stress the need to implement analytical frameworks for population management that explicitly consider the uncertainty about the behavior of natural systems.     

Option value under income and price uncertainty

We present a rigorous examination of the sign of option value under income and price uncertainty. We state and prove three theorems on the sign of option value when preferences are state independent. If income is uncertain, the sign of option value is opposite the sign of the income elasticity of the good in question. The analysis of price uncertainty is in two parts: one covers the case of own price uncertainty and the other the case where the price of some other good is uncertain. In both cases the sign of option value is generally ambiguous.     

Simulated Responses of a Forest-Interior Bird Population to Forest Management Options in Central Hardwood Forests of the United States

I used estimates of carrying capacity, survival, fecundity, and edge effects to simulate the responses of a forest-interior bird population to selection cutting clearcutting, and no timber harvest. I also modeled population sensitivity to changes in fecundity, survival, K , and edge relationships. Because model parameters are based on scant data, results should he regarded as hypotheses to be further investigated or measures of the relative impact or sensitivity (given model assumptions). Simulated population size was greater with no timber harvest than with clearcutting and greater with clearcutting than with group selection when edge effects were included in the model. Without edge effects, population levels were only slightly lower under group selection than under no timber harvest, and greater than clearcutting. Edge effects had only a small impact on population levels under clearcutting. Clearcut size did not have much effect on population levels, but longer and shorter rotation ages resulted in higher and lower population levels, respectively. The model was very sensitive to declines in mean fecundity and survival, suggesting that factors affecting mean demographic rates could be more important than local edge effects. Some methods of timber harvest may be compatible with the conservation of forest-interior birds, but better demographic data and information on habitat suitability of selectively cut forests and young even-aged stands is needed to adequately evaluate management options.     

Ungulate population dynamics and optimization models

Optimal harvesting strategies for an ungulate population are estimated using stochastic dynamic programming. Data on the Llano Basin white-tailed deer (Odocoileus virginianus) population were used to construct a 2-variable population dynamics model. The model provided the basis for estimating optimal harvesting strategies as a feedback function of the current values of the state variables (prefawning older deer and juveniles). Optimal harvest strategies were insensitive to assumptions about the probability distributions of the stochastic variable (rainfall). The response of the population components to harvesting and the returns obtained from applying optimal strategies were explored through simulation. Mean annual harvest is about 15% of the population. Simplified harvesting strategies based on age-ratios as well as a simplified version based on optimal strategies—but assuming persisting equilibrium juvenile deer density—were compared to optimal strategies through examining values of information. Simplified harvesting strategies lead to a lower harvest over a 50-year simulation period.     

Uncertainty,benefit-cost analysis,and the treatment of option value

This paper proposes a new conceptual framework for defining welfare measures under uncertainty: the planned expenditure function. This function describes the locus of expenditures on contingent claims that are required to realize a given level of expected utility. To illustrate the convenience of the framework, it is used to consider the definition of the option price, the appropriate treatment of option value, the valuation of risk changes, and the definition of non-use benefits under uncertainty.     

Utility maximization and catasphore aversion: A simulation test

Economists have proved that the exclusion of the effects of irreversibility from a decision-making framework is a specification error which leads to sub-optimal solutions. Consequently, in any cost-benefit framework, the effects of an irreversibility are included in the form of an option value. Unfortunately, in the real world, there exist certain potential irreversibilities that jeopardize the very existence of the decision-making entity, were they to occur. We demonstrate that if the effects of such irreversibilities are modeled in terms of a finite option value (in cost-benefit analysis) then the optimal solutions derived therefrom may be unable to avert a potential catastrophe. In theory, an infinite option value should lead to catastrophe-averting decisions in such situations. However, in practice, such mathematical formulations tend to be intractable. In many situations, irreversible catastrophes proceed from a positive reinforcement of fluctuations in system behavior, primarily due to sympathetic responses in sub-systems. Engineers have designed relatively low-cost methods to dampen similar oscillations in physical systems. We demonstrate how such engineering type analysis can be used successfully to identify catastrophe-averting policies for a model ecosystem that faces irreversible famine that must be avoided as a precondition for survival.     

Strategic climate policy with offsets and incomplete abatement: Carbon taxes versus cap-and-trade

This paper provides a first analysis of a “policy bloc” of fossil fuel importers which implements an optimal climate policy, faces a (non-policy) fringe of other fuel importers, and an exporter bloc, and purchases offset from the fringe. We compare a carbon tax and a cap-and-trade scheme for the policy bloc, in either case accompanied by an efficient offset mechanism for reducing emissions in the fringe. The policy bloc is shown to prefer a tax over a cap, since only a tax reduces the fuel export price and by more when the policy bloc is larger. Offsets are also more favorable to the policy bloc under a tax than under a cap. The optimal offset price under a carbon tax is below the tax rate, while under a cap and free quota trading the offset price must equal the quota price. The domestic carbon and offset prices are both higher under a tax than under a cap when the policy bloc is small. When the policy bloc is larger, the offset price can be higher under a cap. Fringe countries gain by mitigation in the policy bloc, more under a carbon tax since the fuel import price is lower.     

An Economic Analysis of the Fisheries Bycatch Problem

Bycatch is the incidental take of a species that has value to some other group. This paper compares open access and individual transferable quota equilibria to the equilibrium in which the joint value of the fisheries is maximized. The open access induced problems can be corrected by an individual transferable quota system only if both the target species and the bycatch species have tradable quotas, and only if the bycatch species does not have existence value. There exists a range of the bycatch-to-target species harvest levels for which the total harvest of each will be exactly taken by a given technology, even under open access. However, there may not even exist a unique open access equilibrium if bycatch is allocated by “rule of capture.” Prohibitions on the sale of bycatch reduce the bycatch level, but they also reduce social welfare.     

Enforcement and price controls in emissions trading

This paper examines how enforcement affects the structure and performance of emissions trading programs with price controls under uncertainty about firms' abatement costs. The analysis highlights how an enforcement strategy can cause abatement-cost risk to be transmitted to enforcement costs via the price of permits. When this occurs, accommodating the effect of abatement-cost risk with an optimal policy results in higher expected emissions and lower expected permit price than their second-best optimal values. However, it is possible to design an enforcement strategy that shields enforcement costs from abatement-cost risk by tying sanctions directly to permit prices. This enforcement strategy stabilizes enforcement effort, the optimal permit supply and price controls are independent of enforcement costs, and the policy produces the second-best optimal outcome.     

Redesigning harvest strategies for sustainable fishery management in the face of extreme environmental variability

Short-lived, fast-growing species that contribute greatly to global capture fisheries are sensitive to fluctuations in the environment. Uncertainties in exact stock–environment relationships have meant that environmental variability and extremes have been difficult to integrate directly into fisheries management. We applied a management strategy evaluation approach for one of Australia's large prawn stocks to test the robustness of harvest control rules to environmental variability. The model ensemble included coupled environmental-population models and an alternative catchability scenario fitted to historical catch per unit effort data. We compared the efficacy of alternative management actions to conserve marine resources under a variable environment while accounting for fisher livelihoods. Model fits to catch per unit effort were reasonably good and similar across operating models (OMs). For models that were coupled to the environment, environmental parameters for El Niño years were estimated with good associated precision, and OM3 had a lower AIC score (77.61)  than the base model (OM1, 80.39), whereas OM2 (AIC 82.41) had a similar AIC score, suggesting the OMs were all plausible model alternatives. Our model testing resulted in a plausible subset of management options, and stakeholders selected a permanent closure of the first fishing season based on overall performance of this option; ability to reduce the risk of fishery closure and stock collapse; robustness to uncertainties; and ease of implementation. Our simulation approach enabled the selection of an optimal yet pragmatic solution for addressing economic and conservation objectives under a variable environment with extreme events.     

The optimal use of non-renewable resources: The theory of extraction

The traditional theory of exhaustion is revised to allow for long run capital mobility. This model is extended to include the impact of cumulative environmental damages on the optimal path of resource use. Models and optimal markets are then analyzed for cases where minerals are available over a continuum of quality and where recycling ameliorates inevitable exhaustion of non-renewable resources. Finally, the impact of technological change on long run trends in mineral prices is examined.     

Conserving spawning stocks through harvest slot limits and no-take protected areas

The key to the conservation of harvested species is the maintenance of reproductive success. Yet for many marine species large, old, individuals are targeted despite their disproportionate contribution to reproduction. We hypothesized that a combination of no-take marine protected areas (MPAs) and harvest slot limits (maximum and minimum size limits) would result in the conservation of large spawning individuals under heavy harvest. We tested this approach under different harvest intensities with a 2-sex, stage-structured metapopulation model for the Caribbean spiny lobster (Panulirus argus). P. argus is intensively harvested in the Caribbean, and in many localities large, mature individuals no longer exist. No-take MPAs and harvest slot limits combined, rebuilt and maintained large mature individuals even under high harvest pressure. The most conservative model (a 30% MPA and harvest slot limit of 75–105 mm) increased spawner abundance by 5.53E¹² compared with the fishing status quo at the end of 30 years. Spawning stock abundance also increased by 2.76–9.56E¹² individuals at a high harvest intensity over 30 years with MPAs alone. Our results demonstrate the potential of MPAs and harvest slot limits for the conservation of large breeding individuals in some marine and freshwater environments. Decisions on which management strategy best suits a fishery, however, requires balancing what is ecologically desirable with what is economically and socially feasible.