MEY for a short-lived species: A neural network approach
Introduction
Maximum Economic Yield (MEY) occurs at catch levels where the net benefit from fishing, measured in terms of the difference between total benefits and total costs, is maximized. Depending on how benefits and costs are defined, management authorities can calculate and use MEY to regulate individual fishing behaviour consistent with overall commercial, social and environmental objectives. Calculation of MEY must account for all of the external effects of individual fishing behavior, on both the fishery and other fishers, and if the fishery is not regulated these effects often lead to economic overfishing and rent dissipation.
The two external effects that have been most commonly discussed in MEY studies are contemporaneous and dynamic-stock effects (Chu and Kompas, 2014). A contemporaneous effect arises when the catch of any one fisher reduces the stock available to all other fishers and consequently lowers the catch rate overall. A dynamic-stock externality occurs when catch in any given year has long-term effects on the fishery via reducing (spawning and other) stocks, thus altering stock dynamics in the following years. This long-term effect implies that the key driver of stock abundance is catch history, and not only catch in the same or any given year. In this case, any plans to drive the fishery to MEY, or any other benchmark, normally require concerted effort for more than one year, regardless of whether there are environmental factors that can influence stock abundance. This is why most, if not all, of the models developed by economists to determine or analyse MEY are formulated as dynamic optimization problems (Clark, 1973, Clark, 1990; Clark and Munro, 1975; Grafton et al., 2007, Grafton et al., 2010, Grafton et al., 2011; Kompas and Che, 2006; Kompas et al., 2011).
Nevertheless, there are many important commercial fisheries that, in practical terms, are not subject to the long-term effect of fishing. This situation arises when the lifespan of a species is less than a year, or a fishing season, so uncaught stock does not survive until the next year or season, or when a species can live more than one year, but uncaught stock neither spawns, nor remains commercially valuable. Cephalopods (e.g., squids) and shrimps (or prawns) are the two most important short-lived species in world fisheries, with catches increasing steadily during recent decades (Clarke, 1996), accounting now for total worldwide catches second only to tuna (FAO, 2014). Their short lifespan and fast growth mean that there is little overlap across generations, catch availability is heavily dependent on environmental conditions for growth and survival, and the species is inherently resistant to fishing pressures (Boyle and Rodhouse, 2005; Gillett, 2008). As long as there are no incentives or opportunities for spawning stock depletion, the impact of catch history on the stock availability of a short-lived species is small relative to environmental factors, which indeed often affect if not diminate stocks. This has been documented in many studies, for example, the impact of temperature on squids (Chen et al., 2007; McInnis and Broenkow, 1978; Robin and Denis, 1999), or the impact of rainfall on prawns (Gillett, 2008; Haywood and Staples, 1993; Meager et al., 2003).
The absence of a dynamic stock effect and the significant influence of environmental factors has a number of implications for determining MEY in these important fisheries. For short-lived species, economic overfishing does not generate a practical risk of non-recoverability, but effort creep and race to fish behaviour can drive catch far above what is an economically optimal level. While the overall objective is still to maximize the net benefit by controlling for externalities that the fisheries are subject to, calculating MEY for short-lived species does not require modelling of the long-term effect of catch on abundance. On the other hand, the calculation of MEY must take into account environmental factors that can vary from year to year, or within season, and greatly influence stock availability. For this reason, the rule to determine MEY for short-lived species must be principally adaptive to how environmental factors unfold.
There are two general approaches to account for environmental factors in prawn fisheries (Gillett, 2008, p. 85), and their principles are applicable to other short-lived species. The first approach is based on catch per unit of effort (CPUE) which has been adopted in many, if not most, shrimp fisheries in developing tropical countries because it is simple, easy to use and understandable to both fishers and the public (Gillett, 2008). From an economic perspective, the use of CPUE reflects a fundamental principle, namely catch should occur until marginal revenue equals marginal cost. For example, if fish prices are constant at $4000/ton and the fishing cost is $8000/day, then the break-even CPUE will be 0.5 ton/day. The price and cost used to calculate this CPUE target can be updated every year to control for fluctuations in input and output markets. With such a catch-rate rule, the total catch at MEY is neither explicitly specified beforehand, nor realized until the threshold is reached. In favorable conditions, a large quantity of fish may be landed, while in unfavourable conditions, when stock is limited or smaller than ‘normal’, very little harvest is caught before profit starts to fall. Thus, given a constant fish price and the cost of one fishing day, the catch-rate rule chooses the best catch level to maximize profit.
However, due partly to a reliance on a constant price for fish, this simple rule is not always applicable. The quantity of a good brought to market generally affects price, and fish are no exception (Sumaila et al., 2007). This implies that marginal benefits decrease with catch. Economists often use a price elasticity to measure how price varies with catch and if this coefficient is not zero, it gives rise to a third type of externality where consumers are prepared to only pay a lower price for fish when supplies to market increase with catch. The catch-rate rule cannot adequately address this price externality, even when fish prices are updated at the start of the fishing season, to capture market forces that vary throughout the season. An increase in catch and fish supplies will likely reduce the price that consumers are willing to pay, and thus the break-even catch rate based on the initial price may result in overfishing. This problem could be ideally addressed by using the average price for the whole season, but that information will only be available after the season ends because total catch is not realized until the threshold is reached. Favorable conditions, and a good catch, in other words, can reduce the price of fish brought to market and profit may start to fall when the catch rate is still at a profit-making level in years with adverse conditions.
The second approach used in fisheries of short-lived species with significant environmental factors is the use of some index or estimate of recruitment or abundance, based on these environmental factors, thus addressing the limitations of the CPUE approach. The idea is simply to relate stock availability to how environmental factors unfold before each fishing season, and then to calculate the catch that maximizes the difference between the estimated benefit and cost. This approach can be applied whether the price elasticity is zero or not, but its accuracy depends critically on the predictive quality of the catch-effort relationship (i.e., the harvest function), which is determined by the quantitative or estimated relationship between stock availability and environmental factors. The key challenge of this approach is that even if it is possible to obtain data on the environmental factors, it may still be difficult to quantify how these factors influence stock availability, since this relationship is rarely directly observed.
A possible alternative is to use proxies for the stock availability, such as boat sampling data or total catch, to calibrate a connection to environmental factors. However, we usually have too little information to specify a model that can convincingly ‘explain’ the data. The impact of an environmental factor on different reproduction stages of a species is often hard to quantify, and the interaction with its prey and predators (Boyle and Boletzky, 1996; Caddy and Rodhouse, 1998) under confounding environmental factors make the analysis even more complicated. In addition, the predictive capacity of the model may be affected by the poor quality of the proxies. The catch of boats in sampled locations, for example, may not accurately reflect the entire fishery due to high migration rates, or total catch may simply be subject to demand and technology factors rather than the stock availability (Boyle and Boletzky, 1996). For instance, Venables et al. (2011) estimate stock availability in Australia’s Northern Prawn Fishery (NPF) by regressing total catch against rainfall indices, and when used to estimate the harvest function, this may result in underfitting and a technical error in the sense that stock availability can be less than what predicted or actual catch may imply (Buckworth et al., 2014). In another paper, Deng et al. (2015) develop a size-structured model to estimate stock availability, but this model, as noted in its discussion, does not always fit the data well and might also give a forecast where the observed actual catch exceeded the stock availability. Thus, in our work, we have looked outside the traditional toolboxes for complementary techniques that can provide a better quantitative measure of the relationship between stock availability and how environmental factors matter.
The key contribution of our paper is that we show how stock availability and subsequently the harvest function, as well as MEY, for short-lived species can be estimated using a neural network approach. This technique does not require any statistical models to connect environmental factors to stock availability, but can provide good quality predictions nonetheless. The remainder of the paper is organized as follows. In Section 2, we describe the model including the structure of the neural network and the calibration procedure. In Section 3, we show an application where the harvest function and MEY for NPF banana prawns are estimated via the network. Section 4 discusses some implications of the neural network approach including suggestions for future research.
Section snippets
Model specification and calibration procedure
In this section, we present a model to capture the economic components of fishing a short-lived species. To highlight the application of our neural network approach, we only focus on the economic benefit of harvesting a short-lived species and the cost of fishing effort, bypassing the ecological services a species may provide (Hunsicker et al., 2010) and other ecological costs of fishing such as by-catch. We also model MEY as targeted catch (i.e., with an output control) though it can be
Application to Australia’s Northern Prawn Fishery
In the NPF, banana prawns are a short-lived species with a stock availability critically dependent on pre-season rainfall. The current management strategy for banana prawns in the NPF is the catch-rate rule (Woodhams et al., 2011), which may result in overfishing because of the negative correlation between price and catch (Buckworth et al., 2014). In this section, we first provide an overview of NPF banana prawns and then present the estimated harvest function and rainfall-dependent MEY.
Discussion
The two standard approaches to calculating MEY for a short-lived species have different ways of dealing with the impacts of environmental factors. A catch-rate rule tries to find an optimal result by adapting to the environmental impacts as they unfold from season to season, accounting for realized catches, while the ex-ante approach tries to predict the effects of environmental factors given historical and weather-related data. The first approach is simple and does not depend on prediction,
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