توزیع رایگان ایده آل و یا بازی پویا؟مطالعه شبیه سازی مبتنی بر عامل استراتژی تراولینگ با اطلاعات متنوع

An ecological economic model of trawling is presented to demonstrate the effect of trawling location choice strategy on net input (rate of economic gain of fish caught per time spent less costs). Fishing location choice is considered to be a dynamic process whereby trawlers chose from among a repertoire of plastic strategies that they modify if their gains fall below a fixed proportion of the mean gains of the fleet as a whole. The distribution of fishing across different areas of a fishery follows an approximate ideal free distribution (IFD) with varying noise due to uncertainty. The least-productive areas are not utilised because initial net input never reaches the mean yield of better areas subject to competitive exploitation. In cases, where there is a weak temporal autocorrelation between fish stocks in a specific location, a plastic strategy of local translocation between trawls mixed with longer-range translocation increases realised input. The trawler can change its translocation strategy in the light of information about recent trawling success compared to its long-term average but, in contrast to predictions of the Marginal Value Theorem (MVT) model, does not know for certain what it will find by moving, so may need to sample new patches. The combination of the two types of translocation mirrored beam-trawling strategies used by the Dutch fleet and the resultant distribution of trawling effort is confirmed by analysis of historical effort distribution of British otter trawling fleets in the North Sea. Fisheries exploitation represents an area where dynamic agent-based adaptive models may be a better representation of the economic dynamics of a fleet than classically inspired optimisation models.

The management of fish stocks needs to take into account both the biological aspects of the fish population and the behaviour of the fishers themselves. Fishing behaviour incorporates aspects of economics, sociology and information science. A failure to understand these aspects of fisheries management can lead to disastrous breakdowns in the fisheries management system [1]. There are two different approaches to understand the interactions between fishing vessels and marine resources. The top-down or classical approach seeks to explain trawler behaviour by positing relationships between resources and trawling patterns, and the bottom–up approach posits that patterns are best explained by considering how they emerge from interactions between the strategies of the individual and marine resources. The two approaches are complementary rather than contradictory (in an analogous manner to classical and quantum thermodynamics). One fundamental relationship that has been used to explain the distribution of fishing effort [2] and [3] is the Ideal Free Distribution (IFD) model [4]. In this model, there is an explicit relationship between the rate of input (Ij) of a resource into an assemblage of areas and the number of consumers consuming in that area (nj). Considering two patches where α is the exponent of interference, and the subscript denotes the area on which the consumers are feeding. In the simplest case of the IFD, α=1 and the relationship between the ratios of nj and Ij in the two areas is linear. This unitary case occurs when a fixed resource is divided equally between consumers. In many cases, including here, α can be derived from the mechanics of foraging and resource replenishment. A variant on the IFD occurs when travel costs are taken into account, i.e., the distribution is not completely free [5]. Further variants occur when there are perceptual constraints, i.e., the model is not completely ideal and when competitive abilities differ between consumers [6]. A more general distribution model is described by Farnsworth and Beecham [7]. Experimental tests with animals have tended to reveal departures from the IFD, with a tendency for occupation of the better patches [8] and [9]. An alternative approach to understanding forager-resource distributions uses game theory. Where there are N foragers, each is expected to choose, sequentially, one of M areas, whose resources they share with others in that area, always ensuring that the area chosen gives the best return. When there are many more foragers than patches, the Nash equilibrium results in an intake per patch that is almost identical for all foragers. But when N is only slightly greater then M and the number of occupants of each patch must be quantised to a whole number of occupants, so some individuals will fare worse than others. In such a case, there may be systematic differences in patch choice between animals of different competitive abilities [6]. One pertinent objection in the case of biological systems is that the agents themselves are not able to understand the function which must be optimised, which necessarily includes many other agents and biological processes. From the standpoint of the individual, the problem is formally incomputable. However, the IFD can be achieved by relatively simple switching rules; e.g., Milinski [10] showed that a simple comparison with experience could lead to an IFD in sticklebacks. Maynard Smith [11] argued that a learning system that could cope with change necessarily involved sampling of seemingly unattractive patches. Thuusman et al. [12] showed that sampling rules that led to an IFD and a Pareto optimum for large populations led to a departure from that optimum for individuals. In the case where the IFD results from learning, it should be considered as an emergent or teleonomic property of foraging choice rather than a mechanistic solution to a foraging problem. In essence, there are two ways of looking at the distribution of vessels, as a paradigm involving assessment of the situation and active choice by the fishermen (the ‘ideal’ in ‘IFD’) and as an emergent property of a system where the information available to the trawlers is less complete. There is a similar dichotomy in approaches between classical and agent-based economic models. In neo-classical economic models, from which the IFD model draws its inspiration, there is an implicit assumption of rationality [13]. By contrast, economic models inspired by statistical mechanics have assumed that the rationality is bounded by the information available to each agent. Such models include the El Farol problem [14] and Minority Game [15] and [16]. They predict that the system will attain a statistical equilibrium around which every state transition decreases payoff from an assemblage of agents with incomplete information. This information is historical and agents cannot pre-empt the decisions of their competitors. This is a much more compelling paradigm for the problem of resource uses by competing fishers than one that assumes rationality. In particular, it agrees with data from surveys of fishers, which showed that previous location of trawling was the most important predictor of subsequent trawling activity [17]. Here, we describe a game theoretical framework that is similar to the Minority and El Farol games in that fishers compete to try to exploit patches with sufficiently few competitors that their intake is at or above average, but where the system tends to evolve towards the Nash equilibrium. However, the equilibrium of the game is dynamic because agents must act on historic information. The fisheries game differs from the Minority Game in two important respects: there is spatial correlation between fish abundance in adjacent patches and there may be correlation between the amount of fish at different times. Furthermore, there is an ensemble of strategies that are not equivalent in how they respond to both temporal and spatial lag. The spatial and temporal variation between populations of different fish stocks is known to be species specific, so the optimal strategies for exploiting different fish stocks are expected to vary. The IFD can be viewed as a statement of correspondence between resources and distribution, i.e., to what extent does the real distribution of fishing effort correspond to Eq. (1). It can also be viewed as a model of how boats may find their resources given assumptions about how they compete and process information: that they are free to compete with each other for resources and have an ideal amount of information. The model in this paper demonstrates that the first statement may be true without the second following, because the distribution may result from a process that is not ideal because information is limiting. Examination of micro- and macro-scale data on fisheries in the light of specific model predictions may help us to distinguish between the hypothesis of ideal location choice and an emergent equilibrium based on the aggregate properties of a population of differing simple strategies

In considering the origins of the IFD amongst fishing vessels, it is necessary to consider the nature of interference between vessels [3]. The model presented in this paper has used a model of the depletion of a fixed stock of resources rather than that of a continuous input of new resources. The result of this change from the original IFD assumptions is to make the interference between vessels within patches a function of time. But time is also implicit in the strategy of a single vessel in how it balances time spent trawling, moving and sampling. However, the solution of marginal value calculation (Eq. (12)) requires knowledge of the whole fishing trip, including competition from other boats, information that will not generally be available. For this reason, we look to a framework where the decisions can be made by choosing the most appropriate simple rules, together with an evolutionary framework, to allow this set of rules to be improved upon. We have shown that a statistical mechanical approach to modelling fisheries utilisation by trawlers is able to encapsulate many of the features of the decision-making dynamics of trawlers. Specifically, we outline how the dichotomy between the habit of returning to former fishing grounds and of exploratory and sampling behaviour depend on the stability of information about locality of fish stocks. This model of foraging has revealed how the IFD may be an emergent result of a simple comparison, rejection and random choice strategy that does not require understanding of the current distribution of boats and does not require explicit foreknowledge of the distribution of resources. Trawl fishers succeed, both in the simulation and in real life, by adopting a plastic set of strategies that can be chosen and discarded in light of evidence as to their success. Furthermore, a distinction can be made between fishing tactics and fishing strategy [29] with variability in the former being associated with low catches (i.e., fishers are more likely to switch tactics following lack of immediate success). There is no need for explicit knowledge as to the location of any stock, as demonstrated by the ability of trawlers to obtain a high rate of return with an ephemeral stock by adopting a suitable translocation strategy. However, when dealing with uncertainty, the use of historical information about rates of returns is important in evaluating success. The effectiveness of a strategy built largely upon strategic shifts in rigid strategies versus plastic response to local information depends upon the circumstances of the fishery. Fish stocks vary considerably in their predictability [30], with cod and haddock stocks tending to have predictable year on year distributions and whiting less so. This simulation work has demonstrated that by choosing between a repertoire of more or less plastic strategies, trawlers can match their effort distribution to stocks that are either long-term predictable or long-term uncertain. The exploration of this model has revealed that our understanding of the pattern of spatial resource use by trawlers critically depends on scale, both in terms of the rate of depletion of resources and the time frame over which the pattern of fish distribution varies. Rijnsdorp et al. [31] reported that in some parts of the North Sea half was trawled annually and about 15% trawled 4 or more times a year by the Dutch beam trawl fleet. The implication of this is that if our epoch time is around a year, the total fishing mortality may vary from between 0.5 and over 1 and depletion of local stocks is significant, so there is potentially considerable interference between boats. The use of cpue as a measure of fish stocks has been characterised as problematic [32]. When a patch is initially exploited, catch is indeed proportional to the stock density times the effort, but the solution of the IFD implies equalisation of cpue between patches [33]. A small amount of interference can lead to a breakdown in the cpue—catch relationship [34]. On the other hand, if both temporal and spatial scales are at their largest, then cpue is a useful indicator once again. In other words, if the mean stocks across the whole fishing ground are reduced equally by a factor but the total fishing mortality is kept the same (nsT remains constant), V(T) is reduced by that same factor. There are a number of mechanisms that could be incorporated into this statistical mechanical framework. One is the degree to which information is shared between vessels, either intentionally or by copying. The advantage of information sharing is that it reduces the time losses attributable to searching [35]. On the other hand this increases the overmatching losses in the best patches and leads to more rapid depletion. Imitation behaviour is useful only so far as it reduces the costs of sampling poor patches and helps the trawler find good ones (i.e., it serves to increase nr until it satisfies Eq. (10)) but it is a progressively less effective strategy as good patches are overfilled. Millischer and Gascuel [36] showed that there was a trade off to information sharing, which was more beneficial for smaller groups and more aggregated resource distributions. However, where information sharing would appear to be advantageous in terms of catch quantity, trawlers operating in a heterogeneous mixed fishery may be at a disadvantage by following others because they will obtain more fish of species that are abundant in the market as a whole. The desire to find fish under represented in the market may be an explanation for apparent slightly risk-prone behaviour of fishers [17]. The tendency to copy or innovate could also be part of the repertoire of strategies subject to rejection and reinforcement. In practical fisheries management, repertoire models are useful for risk analysis because they can allow for a range of possible trawler responses to changes in circumstances (changes in fish stocks, closure of fishing areas) and allow the model trawlers to select their optimal strategy from their repertoire. The optimal strategy is likely to be the one leading to greatest concern for fisheries managers. A strength of the object simulation framework used is that it can incorporate heterogeneity among the fleet. Differences in competitive interactions may lead to asymmetry in patch choice between trawlers of different competitiveness [6], in addition the optimum fishing area may be different for boats of different powers [2]. The pattern of fishing restrictions and closed areas is likely to affect the economic balance between boats of different sizes, indeed many of the fishing restrictions have exemptions specifically to allow fishing by less powerful boats. A game theoretical economic model is a potential powerful tool to examine the implications of fisheries area management for favouring or disfavouring a greater number of less competitive boats over fewer more modern and powerful boats, for example. The examination of short-term competitive trawling tactics can also be used to examine implications arising from optimal fishing strategy, such as discards [37]. The main difficulty of examining heterogeneity is the potential vast range of combinations of behaviour. However, the model would be suitable for answering questions such as the strategic significance of allowing only low-powered vessels to fish in restricted areas. A fully spatially explicit model will need a greater repertoire of behaviours to cope with the increased dimensionality of vessel movements. The arrangement of the resources in relation to the starting points will vary from partially circular where the port is on a headland (e.g., Peterhead in North East Scotland) to linear where there are several ports along an approximately linear coast—the North East coast of England for example. It is suggested that a two-dimensional model should be an explicit geographical model and used with specific data rather than the more abstract type of model presented here. The one-dimensional movement model will need to be replaced by one that considers the distribution of both distance and direction. One candidate for a movement model, in one or two dimensions, is the Lévy flight model, which has been used in the characterisation of movement of a variety of animal species [38] and [39]. Its most distinctive feature is that compared to Brownian diffusion, the upper tail is exponential, so that some movements are very much longer than the median. The probability of making a move of distance dm is proportional to (dm+dmin)−μ. The fractal dimension of the Lévy flight is μ. The attraction of this model is that it represents the probability of a trawler adjusting spatial scale. Altering the value of μ always allows for some movement at the longest scale but reduces the probability of this happening. Another important property is that for multiple foragers with the same start points (i.e., ports) the Lévy model predicts a higher efficiency at discovering exploitable sites within an area; the long jumps spread out the fleet over a wide area, the small jumps ensure that the area around a point is exploited. The Lévy flight model has been applied to fishing movements of trawlers for anchovies [40], with the value of μ being between 1.61 and 1.84 and a little higher than the fractal dimension of the anchovy stocks. In North Sea fisheries, a Lévy flight model with a value of μ varying over a range from 1.1 to 1.8 for inter-haul distance was identified [41]. It is possible to compare trawling strategies with the distribution of fish resources and determine economically optimal fishing behaviour. Investigation could be undertaken to see to what extent having a foraging decision model that matches the pattern of the resources obviates the necessity of a mixed strategy implicit in the El Farol model. An equally important area of extension of the model is in the development of an economic model with agents who interact with the vessels via a market. In the historical British steam trawl data, there appeared to be market mechanisms that led to equality in value per unit effort for different fish stocks. The mechanics of that market are important in conservation because a high degree of price elasticity of demand and a low degree of substitutability of different fish species will lead to continued fishing of a depleted stock even when cpue is low. The increased value of bluefin tuna stock in the Japanese sashimi market, for example, seems to have been instrumental in its increased exploitation [42]. A related area of interest would be the costs and benefits of illegal fishing, in relation to its perceived benefits and perceived costs that are likely to vary between individuals. Criticism has been made of the use of Minority Game type models in economics, because they do not allow for expansion of the market and synergy between agents leading to growth [43]. However, these criticisms would not seem valid for purely exploitative industries, such as fishing, where innovations in extraction do not lead to a greater overall level of extraction in the long term. This is truer of fishing than of mining. In conclusion, an approach to modelling fisheries inspired by statistical mechanics provides a compelling framework for understanding how fishers cope with limited information. However, a Minority Game type of patch choice mechanism is only one aspect of the way in which trawlers interact. Other aspects might include imitation of strategies and individual or collective optimisation of strategies that may lead to improvement of trawling effectiveness. Set against this is the dynamics of fisheries management, for example, closing of specific fishing grounds necessitating a strategy switch. This modelling work suggests that the prediction of an IFD may be relatively robust to the optimisation methods fishers use, and especially where stocks are inferred from catch and effort, is not necessarily indicative of complete knowledge of the system (and so it is not, sensu stricto, ideal). The evidence of much sampling behaviour by fishers at short temporal and spatial scales, but less sampling over a whole 30 nautical mile rectangle over a year, suggests that the trawlers were more ideal at larger scales in the 1930s but may be less so in recent years.