Information flow among fishing vessels modelled using a Bayesian network

Environmental Modelling & Software 19 (2004) 27 34 www.elsevier.com/locate/envsoft Information flow among fishing vessels modelled using a Bayesian network L.R. Little a,, S. Kuikka b, A.E. Punt a,c, F. Pantus d, C.R. Davies e, B.D. Mapstone f a CSIRO Marine Research, GPO Box 1538, Hobart, Tasmania, Australia 7001 b Finnish Game and Fisheries Research Institute, P.O Box 6, FIN-00721 Helsinki, Finland c School of Aquatic and Fishery Sciences, Box 305520, University of Washington, Seattle, WA 98195-5020, USA d CSIRO Marine Research, PO Box 120, Cleveland, Queensland, Australia 4163 e National Oceans Office, GPO Box 2139, Hobart, Tasmania, Australia 2139 f CRC Reef Research Centre, James Cook University, Townsville, Queensland, Australia 4811 Received 17 November 2002; received in revised form 17 March 2003; accepted 5 May 2003 Abstract Reaction of fishers is an essential source of uncertainty in implementing fishery management decisions. Provided they realistically capture fisher behaviour, models of fishing vessel dynamics provide the basis for evaluating the impact of proposed management strategies. Information flow among vessels has not been a major focus of such models however, although it might play a critical role in how a fleet responds to changes to management restrictions or levels of a resource. Such a response might then modify subsequent exploitation of the resource. In this paper, a spatially-explicit model of vessel fishing behaviour is developed for a line fishery on the Great Barrier Reef, Australia. Vessel behaviour is conditioned on past catch and effort data at a spatial resolution of 6 6 nautical mile grid cells. For each vessel, the probability of fishing a particular grid cell is determined from past income per unit effort experienced at that location, and the cost of steaming to it. The probability distribution across all possible grid cells represents a particular vessel s perspective. This perspective is modified by information conveyed by other vessels using Bayesiannetwork information propagation. The information conveyed is the effort distribution of other vessels and is equivalent to a vessel watching where other vessels fish. We compare the behaviours that vessels display when they act independently with those they display when they watch each other, and show the effect that such information flow can have on a resource. Information flow among fishing vessels can be shown to have an effect on the dynamics and resource exploitation of a simulated fishery. 2003 Elsevier Ltd. All rights reserved. Keywords: Influence networks; Belief networks; Management strategy evaluation; Fisheries 1. Introduction Spatially-explicit simulation models are useful tools for assessing the efficacy of spatially-structured fishery management options. Such models consist of at least a fish (meta) population model, and a model of fisher behaviour. Although, traditionally, most research has been directed to the former, understanding fisher behaviour is becoming increasingly necessary as scientists and managers recognize the importance of fisher reactions to management decisions. Hilborn (1985) recognized this, Corresponding author. E-mail address: rich.little@csiro.au (L.R. Little). and resolutely concluded that two major fishery disasters were due to poor understanding of fisher dynamics, not fish biology. Although there are many aspects to fisher behaviour (Hilborn, 1985), where and how fishers allocate their effort is crucial to evaluating the effects of potential management decisions. Previous efforts at modelling fisher effort allocation have addressed many of the complexities inherent to the task. Hilborn and Walters (1987) simplified individual fisher behaviour by modelling effort allocation at the fleet level. Mangel and Clark (1983) modelled search and cooperation of a fishing fleet, and Allen and McGlade (1986) explored the implications of having different fishing strategies or behaviours, and information flow among them. Babcock and 1364-8152/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/s1364-8152(03)00100-2

28 L.R. Little et al. / Environmental Modelling & Software 19 (2004) 27 34 Pikitch (2000) used dynamic programming to model targeting decisions in a multi-species fishery, and Dreyfus- León (1999) applied a neural network to model fisher spatial-allocation decisions. Agent-based models attempt to capture population dynamics through the combined behaviour of a collection of individuals (Uchmański and Grimm, 1996). Thus, agent-based models of fishing vessel dynamics attempt to represent the decisions and actions of individual vessels (Dreyfus-León, 1999). This allows important vessel characteristics that are not easily captured in an aggregate fleet model to be considered. For example, vessels have different home ports, which may be close to or far from certain fishing grounds, affecting the ease with which they can can gain access to them. Although agent-based models embrace individual variability, they must also capture the social interactions among agents. In reality, social interactions among fishers, such as the sharing of catch information, may have a large impact on where vessel operators direct their effort (Palmer, 1991). Bio-economic models that simulate individual fishing vessel dynamics, therefore, must capture these social interactions as they pertain to decision-making processes. In this paper we create an agent-based model of fishing dynamics in which vessel behaviour is modified by information received from other vessels. We use a Bayesian belief network framework to model the information flow among vessels. Bayesian belief networks can be used to model reasoning by using information from a range of sources (Charniak, 1991). They have been applied mainly to decision support and analysis (Kuikka et al., 1999), and there has been little attempt to incorporate them into simulation models, such as those used in fisheries. Because the framework developed by Varis (1998) can be implemented simply within an agent-based simulation model, we use this framework to model information flow among individual vessels in a simulated fishery. Under this framework, vessels use information obtained from other vessels when making decisions on where to fish. In particular, we judged that vessel operators in a hypothetical fishery may be more likely to obtain information by watching where other vessels fish, and so we assumed that the information obtained by a vessel came from other vessels effort distributions. The observation of other vessels in an area was interpreted as evidence of fishing success in that area and vessels were attracted to, rather than repelled from, areas where they saw other vessels fishing. By modelling the behaviour of individual vessels with characteristic home port locations, fishing strategies, and information transmitted passively from other vessels by observing them, we show what effect these characteristics have on the dynamics and resource exploitation of a simulated fishery. 2. Materials and methods The hypothetical fishery we examine is based on the common coral trout (Plectropomus leopardis) fishery on the Great Barrier Reef (GBR). The software and model framework is the Effects of Line Fishing Simulator (ELFSim Mapstone et al., in review). 2.1. The ELFSim model and an overview of its biological component ELFSim is a decision support tool designed to evaluate management options for the common coral trout (Plectropomus leopardis) fishery on the Great Barrier Reef (GBR), Australia. It contains several components, including output visualization and run management, but the most important components are a spatially-structured biological model of coral trout population dynamics, and a model of fishing behaviour. These operate at a monthly time scale, and each simulation consists of two parts. The first part involves generating the abundance on each reef from 1965 to 1998 using information from visual surveys, catch records, and the physical characteristics of the reefs. The second part involves projecting the population on each reef forward in time based on userspecified inputs such as the total annual effort and any spatial and temporal management restrictions. The total annual effort, specified by the user, is converted to monthly effort based on observed historical seasonal effort distributions. The monthly effort is then allocated spatially at the level of 6 6 nautical mile grid cell, the scale at which the commercial catch and effort data are reported. The effort assigned to a grid cell is then allocated among reefs in proportion to their mapped perimeter in that grid cell. Grid-specific effort then determines reef-specific catch, which in turn determines the future size of the reef-specific populations in the biological model. In common with previous models of coral trout on the GBR (Mapstone et al., 1996; Campbell et al., 2001), the biological component of ELFSim is based on the assumption that coral trout comprises a meta-population containing local populations associated with a single reef and linked through larval dispersal. The assumption of dispersal is based on a lack of evidence for movement of animals one year and older from tagging (Davies, 1995). Account is taken of the age, sex, and size-structure of the population on each reef. The number of animals settling each year is determined by the size of the reproductive component of the population, an assumed larval dispersal pattern and density dependence in first-year survival (Mapstone et al., in review). The biological component of ELFSim also allows for natural variability in several population dynamics quantities (e.g. natural mortality and larval survival) as well as variability in the relationship between fishing effort and fishing mortality.

L.R. Little et al. / Environmental Modelling & Software 19 (2004) 27 34 29 2.2. The vessel dynamics model The monthly effort is allocated among grid cells using an individual-based model of vessel fishing dynamics. The key vessel characteristics that influence where a vessel fishes are the past monthly catch-per-unit-effort (CPUE) experienced by the vessel, the location of its home port, and the cost of movement. These variables combine to create a relative attractiveness of each grid cell g, (the relative probability of fishing the grid cell) for each vessel v, during month m: P g,m v a(price CPUE g,m v cost v dist g x v ) (1) where dist g x v is the distance between grid cell g and the home port of vessel v. CPUEn g,m is the historical catch, in kg of fish per day, for vessel v, fishing in grid cell g during month m. If catch data for a grid cell are available for several years, the older data are down-weighted relative to the more recent data (0.9 discount rate). Grid cells that have no historical catch and effort data are assigned a constant probability (1/number of grid cells) so that it is possible to fish areas that have never been fished. Price is the price of 1 kg of coral trout (assumed here to be independent of fish size, location and time), and cost n is cost of vessel v steaming one nautical mile. To keep the model simple so that the units of both the revenue and cost terms of Eq. (1) are equivalent, the vessels are forced to return to port each day (i.e. each fishing trip lasts a single day). a is a scaling coefficient chosen so that the sum of Pv g,m across all grids is unity. Vessels in the model exhibit one of two fishing strategies ( Cartesian or stochast sensu Allen and McGlade, 1986). Cartesians are risk averse, and choose grid cells with the maximum possible return, i.e. the mode of the distribution in Eq. (1). Stochasts are less risk averse and direct their search randomly based on Eq. (1). That is, grid cell g is fished with probability proportional to the profit it is expected to return. Effort is allocated by randomly selecting a vessel, then selecting a grid cell based on its relative attractiveness (determined using Eq. (1)), and the vessel s fishing strategy. This grid cell is allocated one unit of effort. Vessel and grid cell selections are repeated until all of the available effort is allocated. Although vessels are expected to make decisions based on their experience, the available catch and effort data are currently not vessel specific. All vessels therefore, begin with the same historical CPUE information. Because Cartesians are deterministic and all start with same historical CPUE information, future spatial allocation of such vessels is due to the home port from which they operate and the information they receive from the stochasts. 2.3. Information flow Where a vessel fishes is not only influenced by its perceptions of expected profitability, but also by information obtained by observing where other vessels fish. Under the Bayesian Network framework of Varis (1998), the degree of information flow depends on a link parameter (scaled between 0 and 1) that specifies a link matrix. The higher the value of the link parameter, the more information is shared between two vessels. This would translate into greater similarity among vessels expected profitability across grid cells. Based on the assumption that skippers would be more likely to observe vessels from home ports nearby, than from home ports farther away, the value of the link parameter was inversely related to the distance between the home ports of the vessels sharing information. Specifically, the value of the link parameter, L, between vessels a and b is given by: L a,b e k 1 d(a,b) k 2 (2) where k 1 reflects the spatial effect on the link parameter of vessels with different home ports, d(a,b) is the distance between the home ports of vessels a and b, and k 2 is a parameter to change the degree of information sharing. The effort information from other vessels is then used to update the expected profitability information of the vessel making a decision. Based on Varis (1998), the posterior probability of vessel a (one of n vessels) fishing grid cell g (one of n r possible grid cells) during month m, Qa g,m, is given by: Qa g,m ãpa g,m M a,b g,heb h,m (3) b h where M is the link matrix between vessels a and b M a,b g,h 1 n r L a,b (1 1 n r ) 1 n r 1 1 1 n r L a,b (1 1 n r ) ã is a scaling constant, and Eb h,m in grid cell h during month m. 2.4. Scenario considered if g h otherwise (4) is the effort of boat b A single simulation was implemented with vessel dynamics parameters selected to show the type of behaviour that can occur in the individual-based model, with different fishing strategies and information flow among vessels. Fig. 1 shows the 106 reefs on which the analyses of this paper are based. The cost of movement for all vessels, sale price of the catch, and the coefficients gov-

30 L.R. Little et al. / Environmental Modelling & Software 19 (2004) 27 34 Fig. 1. Area of Great Barrier Reef considered in the analyses of this paper. erning the link parameter were set at $10/nautical mile, $15/kg, and k 1 = k 2 = 1.5, respectively. The future projections considered the years 1999 2025 and the fishing fleet involved 12 hypothetical vessels with a combined total annual effort of 4320 boat days. This is approximately equal to the peak annual effort for the area of 4000 boat days. The 12 vessels consisted of four boats (two stochasts, two cartesians) in each of three home ports (Cairns, Port Douglas, and Innisfail). Information flow between the two fishing strategies was not symmetrical; the effort allocation decisions for cartesians were influenced by the effort distribution of stochasts, but not vice versa. Stochasts were therefore influenced only by other stochasts. The behaviours of only four vessels (three with a home port of Cairns (2 stochasts and 1 cartesian), and the other a stochast with the home port of Port Douglas) are shown to keep the volume of results to a manageable amount. Also, although reef-specific biological information is available in ELFSim, for brevity it is not reported here. 3. Results Fig. 2 shows the total available biomass across all reefs, relative to the pre-harvest (i.e. 1965) available biomass, and the corresponding catch for all 12 vessels in the projection period, relative to that in 1998. (The available biomass is the biomass of those fish larger than the minimum legal size that are selected by the fishing gear.) The available biomass is half its pre-harvest level at the start of 1998. The time-trajectories diverge thereafter due to the impact of differences in information flow among vessels. Information flow tended to produce a slightly lower available biomass, and greater catch. Fig. Fig. 2. Time trajectories of (a) available biomass relative to its preharvest level (1965 2025), and (b) total annual catch across all vessels, relative to the annual catch in 1998 (1999 2025). Results are shown for analyses with and without information flow among vessels. 3 indicates the distribution of biomass across reefs, and the distribution of effort that lead to them. With no information flow, effort was concentrated in the northern portion of the area [Fig. 3(b)]. In contrast, with information flow, effort was less concentrated, and directed to those grid cells containing the reefs that had the highest available biomass at the beginning of the projection period in 1998 [Fig. 3(c)]. One reason for the differences between Fig. 3(b) and (c) is the impact of information flow on the vessels that adopt the cartesian fishing strategy. Fig. 4 shows the effort distributions of four individual vessels in the final ten years of the simulation. Differences in the fishing strategies are evident from the large number of grid cells covered by the stochasts (vessels 1, 2 and 4), compared to relatively few covered by the cartesian (vessel 3). In the absence of information from the stochasts, the cartesian only allocated effort to grid cells it historically fished, i.e. in the north part of the area. The reason for this is that cartesians do not explore, and so, in the absence of information obtained from other vessels, there was no opportunity to change their perspective.

L.R. Little et al. / Environmental Modelling & Software 19 (2004) 27 34 31 Fig. 3. Available biomass on reefs (shading of reefs) (a) in 1998, and in 2025 with projected effort in the last ten years of the projection period (2016 2025, shading of grid cells) under (b) no information flow, and (c) with information flow among vessels. Fig. 4. The spatial distribution of effort summed over the final 10 years of the projection period, for four vessels acting independently (no information flow, left) and acting on information obtained from other vessels effort distributions (with information flow, right). Vessel 1: stochast, home port Cairns, vessel 2: stochast, home port Cairns, vessel 3: cartesian, home port Cairns, vessel 4: stochast, home port Port Douglas.

32 L.R. Little et al. / Environmental Modelling & Software 19 (2004) 27 34 However, when information flow among the vessels occurred, the cartesian fished areas beyond those it fished historically. Although a truely cartesian fishing strategy is extreme, the results in Fig. 4 demonstrate the importance that external sources of information might have on the behaviour of risk-averse individuals. The spatial nature of the link parameter, and the effect of distance between home ports, is also evident in Fig. 4. Specifically, when there is information flow among vessels, the effort distributions for vessels from the same home port (vessels 1 and 2) were more similar than those for vessels from different home ports (i.e. vessels 1 and 4). This occurred because greater weight was assigned to the information from vessels that have the same home port; vessels that have close home ports use each others information to a greater extent and hence tend to direct their effort to the same grid cells. Fig. 5 shows the annual catch and profit, summed across vessels in each fishing strategy. The effect of information flow among vessels was to reduce the difference in annual catch and profit between the strategies. This convergence arose mainly because the catch and profit of the risk-averse cartesians increased as a result of fishing grid cells beyond those that were fished historically. However, the catch and profits of the stochasts were reduced, perhaps as a result of lower resource availability due to competition from the cartesians. 4. Discussion Modelling individual vessels allows for individual variability in decision-making and information pro- cessing, which leads to a more accurate description of the behaviour of the fleet (Dorn, 2001). Although this type of independent behaviour in fishing agents is a desirable feature of individual-based models, agents must be able to influence where others fish (Palmer, 1991; Vignaux, 1996). Previous models have shown the importance of vessel interactions and information flow (Allen and McGlade, 1986; Maury and Gascuel, 2001), and this paper outlines a novel means by which individuals can interact in an agent-based model. In the present model, individual vessel decision-making is influenced by the characteristics: home port, fishing strategy, cost of steaming and the relative success experienced by fishing different locations. The vessels interact by obtaining information about where other vessels are fishing. Similarly Vignaux (1996) found that trawlers fishing for hoki (Macruronus novaezelandiae) off New Zealand do not share catch information, but base their decisions on their own catches, and where other vessels fish. This is analogous to spying, and represents just one possible source of information that fishers can use to augment their knowledge about where to fish. Another possible source of information would be the active sharing of catch or CPUE information among vessels, which would be defined as cooperative rather than passive behaviour. Palmer (1991) documented situations in which catch information was shared among lobster fishers off Maine. Relatively high amounts of spying occurred among vessels from the same home port in the present study so that the vessels from the same home port tended to concentrate much of their effort in the same grid cells. Fig. 5. Total annual catch and profit of each strategy relative to those for stochasts at the beginning of the projection period (1999).

L.R. Little et al. / Environmental Modelling & Software 19 (2004) 27 34 33 The distribution of vessels among ports therefore could have a large effect on which areas are fished intensely. Much of the information flow among vessels was restricted to the cartesians watching where the stochasts fished. In the absence of information flow from the stochasts, large decreases in catches and profits were experienced by the cartesians as the grid cells that they continually fished became depleted. When cartesian behaviour was modified by stochasts, the effect was to shift the effort distributions of cartesian vessels away from the areas that were fished historically to areas where stochast vessels fished. This tended not only to reduce the total biomass slightly, but also to reduce the biomass on those reefs that had the highest biomass at the beginning of the projection period. This result is consistent with those from other models (e.g. Maury and Gascuel, 2001) that have concluded fishing efficiency will increase with information flow. Although the strategies used in the model are extreme and oversimplfied, in the context of the individual-based model they comprise a major source of variability among the actors of the simulation. As the model stands, information flow led to more similar catches and profits between the two fishing strategies, and in the absence of information flow, stochasts appeared to have the best catches and profits. Information flow therefore benefited the cartesians and hindered the stochasts. Realistically, a complete absence of information flow among vessels is probably not possible, so determining the optimal strategy, or combination of strategies, that optimize individual vessel profits is a further extension to the model. Furthermore, fishing strategies may not be static, but rather may change as vessel operators consider the strategies of their fellow fishers and adjust their behaviour accordingly. For example, stochasts may have opportunities of discovering large sources of fish, but may also tend to have higher search costs. A vessel under conditions as all the other vessels are stochast, might do better to adopt a cartesian strategy, and simply watch and follow where the successful boats fish. Neither strategy by itself would be evolutionarily stable as suggested by evolutionary game theory (cf. Maynard-Smith, 1982), and determining the stable combination of strategies and the conditions that lead to them represents an important application of modelling interactions among individual fishers. Vessel behaviour can be diversely affected by external sources of information using the Bayesian network approach. For example, a vessel s prior perspective is reinforced when it receives information that indicates other vessels are fishing the places it judges to be the most profitable. This reduces the (perceived) uncertainty of the most profitable places to fish. Alternatively, when a vessel s prior perspective conflicts with where it sees others fishing, the uncertainty in where to fish increases, as two separate beliefs are incorporated into the same probability distribution (Varis, 1998). Thus, information flow among vessels could lead to more erratic fishing behaviour. This was not observed in the results of this paper, perhaps, in part, because vessels began the projection period with the same CPUE information that was used to judge the most profitable places to fish. Unlike Allen and McGlade (1986), no consideration was given to false-information passing among vessels. This was because information flow was based on the passive observation of vessel effort distributions. The propagation of false information would become more important if the exchange of catch information among vessels was incorporated into the model. With the possible transmission of false catch information, vessels would weigh the information they receive from others based on the veracity of their past interactions. This could lead to the formation of vessel alliances, as has occurred in, for example, the Maine lobster fishery (Palmer, 1991). Individual-based models of vessel fishing behaviour incorporate a level of detail that is lacking in more aggregate level models. Information flow is one such detail, and using the Bayesian network framework of Varis (1998), we have shown how information flow among vessels in an individual-based fleet dynamics model can change the spatial allocation of effort, and the level of resource depletion. This underscores the significance of realistically representing fisher behaviour for the purpose of evaluating management strategies. Acknowledgements We are grateful to Tony Smith and David McDonald for their encouragement, support and comments on this work. We also thank the Queensland Fisheries Service for provision of anonymous catch and effort data for the commercial reef line fishery. Funding for the Effects of Line Fishing Project was provided by the Cooperative Research Centre (CRC) for the Ecologically Sustainable Development of the Great Barrier Reef, CRC for the Great Barrier Reef World Heritage Area, the Fisheries Research and Development Corporation, and the Great Barrier Reef Marine Park Authority. This is a publication from the CRC Effects of Line Fishing Project. References Allen, P.M., McGlade, J.M., 1986. Dynamics of discovery and exploitation: the case of the Scotian Shelf groundfish fisheries, Can. J. Fish. Aquat. Sci. 43, 1187 1200. Babcock, E.A., Pikitch, E.K., 2000. A dynamic programming model of fishing strategy choice in a multispecies trawl fishery with trip limits. Can. J. Fish. Aquat. 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