Diversity and complexity of angler behavior drive socially optimal input and output regulations in a bioeconomic recreational-fisheries model

Transcription

1 International Institte for Applied Systems Analysis Schlossplatz 1 A-2361 Laxenbrg, Astria Tel: Fax: pblications@iiasa.ac.at Web: Interim Report IR Diversity and complexity of angler behavior drive socially optimal inpt and otpt reglations in a bioeconomic recreational-fisheries model Fiona D. Johnston (johnston@igb-berlin.de) Robert Arlinghas (arlinghas@igb-berlin.de) Ulf Dieckmann (dieckmann@iiasa.ac.at) Approved by Detlof Von Winterfeldt Director Jly 2011 Interim Reports on work of the International Institte for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institte, its National Member Organizations, or other organizations spporting the work.

2 Diversity and complexity of angler behavior drive socially optimal inpt and otpt reglations in a bioeconomic recreational-fisheries model Fiona D. Johnston 1,2,3, Robert Arlinghas 2,3 and Ulf Dieckmann Evoltion and Ecology Program, International Institte for Applied Systems Analysis, Schlossplatz 1, A-2361 Laxenbrg, Astria 2 Department of Biology and Ecology of Fishes, Leibniz-Institte of Freshwater Ecology and Inland Fisheries, Müggelseedamm 310, Berlin, Germany 3 Inland Fisheries Management Laboratory, Department for Crop and Animal Sciences, Faclty of Agricltre and Horticltre, Hmboldt-University of Berlin, Philippstrasse 13, Has 7, Berlin, Germany 24 25

3 Abstract In many areas of the world, recreational fisheries are not managed sstainably. This might be related to the omission or oversimplification of angler behavior and angler heterogeneity in fisheries-management models. We present an integrated bioeconomic modelling approach to examine how differing assmptions abot angler behavior, angler preferences, and composition of the angler poplation alter predictions abot optimal recreational-fisheries management, where optimal reglations were determined by maximizing aggregated angler tility. We report for main reslts. First, acconting for dynamic angler behavior changed predictions abot optimal angling reglations. Second, optimal inpt and otpt reglations varied sbstantially among different angler types. Third, the composition of the angler poplation in terms of angler types was important for determining optimal reglations. Forth, the welfare measre sed to qantify aggregated tility altered the predicted optimal reglations, highlighting the importance of choosing welfare measres that closely reflect management objectives. A frther key finding was that socially optimal angling reglations reslted in biologically sstainability fish poplations. Managers can se the novel integrated modelling framework introdced here to accont, qantitatively and transparently, for the diversity and complexity of angler behavior when determining reglations that maximize social welfare and ensre biological sstainability Keywords: angler specialization; age-strctred model; harvest reglations; effort dynamics; tility

4 Introdction Recreational anglers are the dominant sers of most freshwater and some coastal fish stocks in indstrialized contries (Arlinghas and Cooke 2009). Accordingly, managers are faced with the challenge of balancing the interests of angling grops tilizing fisheries resorces with concerns abot the biological sstainability of exploited fish poplations (Radomski et al. 2001; Peterson and Evans 2003; Arlinghas 2006b). The lack of sstainable recreational-fisheries management in some areas of the world (Post et al. 2002; Lewin et al. 2006) sggests that crrent management strategies have not always been sccessfl in achieving this balance. This may be becase effectively managing a fishery reqires nderstanding not only how fish respond to exploitation, bt also how anglers alter their fishing behavior in response to social and ecological changes in the fishery; conseqently sch behavioral dynamics mst be incorporated into integrated fisheries-management models (Johnson and Carpenter 1994; Radomski et al. 2001; Post et al. 2008). In the past, however, recreational-fisheries researchers and managers have focsed on the biological dimension of recreational fisheries, largely overlooking the hman dimension (Aas and Ditton 1998; Cox and Walters 2002a; Arlinghas et al. 2008a). To move forward, it is critical to qantify and integrate angler preferences and reslting behavioral decisions into recreational-fisheries models designed to determine optimal management policies (Radomski and Goeman 1996; Arlinghas et al. 2008a). Optimm social yield (OSY) is one management objective that can incorporate social and economic aspects into fisheries-management models and policies (Roedel 1975). In comparison with the traditional approach of managing for maximm sstainable yield (MSY) in both commercial and recreational fisheries 3

5 (Larkin 1977; Malvestto and Hdgins 1996; Hilborn 2007), OSY is better sited to recreational fisheries becase it incorporates socio-cltral benefits a fishery provides that are not measred by yield alone, sch as an angler s satisfaction reslting from catching a large fish (Roedel 1975; Malvestto and Hdgins 1996; Radomski et al. 2001). OSY integrates sch social and economic factors with biological considerations, to develop a fisheries-management objective that maximizes the total tility (alternatively termed benefits or social welfare; Dorow et al. 2010) that a recreational fishery provides to society (Roedel 1975; Malvestto and Hdgins 1996). Hence, similar to MSY, management for OSY may provide an nambigos management objective against which to jdge management developments and sccesses (Bennett et al. 1978; Barber and Taylor 1990; Radomski et al. 2001). Despite the general advantages of a socioeconomic objective sch as OSY over MSY for managing recreational fisheries, few recreational-fishing models based on tility theory have been developed to predict the optimal social welfare generated by different management schemes (e.g., Die et al. 1988; Jacobson 1996; Massey et al. 2006). Frthermore, angler-effort dynamics, if considered at all, are generally assmed to be predominantly or exclsively driven by catch rates, or by some other measre of fish abndance (Johnson and Carpenter 1994; Beard et al. 2003; Post et al. 2003). However, angler behavior is likely mch more complex (Carpenter and Brock 2004; Arlinghas et al. 2008a). It is known from social-science research on recreational fisheries that, in addition to catch rates, a diverse set of social and biological attribtes of a fishery sch as availability of preferred species, fish size, congestion, facilities, reglations and the perceived aesthetic vale of the fishery affect the participation decisions of anglers (reviewed in Hnt 2005). Therefore, angler-effort dynamics driven by catch rates alone can be nrealistic (Palrd and 4

6 Laitila 2004). Hence, recreational-fisheries models designed to maximize angler tility shold accont for complexity in angler behavior by incorporating mltiattribte tility fnctions that describe the fishing-participation decisions of anglers. Another important, yet often overlooked, aspect of recreational fisheries is angler diversity (i.e., heterogeneity in angler behavior; Anderson 1993; Jacobson 1996; Post et al. 2008). Varios types of anglers will differ not only in their fishing preferences, and therefore in the tility they derive from fishing (Fisher 1997; Connelly et al. 2001; Arlinghas et al. 2008b), bt also with respect to their fishing practices (Bryan 1977; McConnell and Stinen 1979; Hahn 1991). Hence, the potential impacts of fishing on fish poplations likely vary with angler type (Dorow et al. 2010). For example, in many fisheries a minority of anglers catches the majority of fish (Baccante 1995), and this minority typically encompasses the most avid and specialized angler types (Dorow et al. 2010). Hman-dimension researchers have repeatedly highlighted that acconting for angler diversity is important for sstainable fisheries management (Fisher 1997; Aas et al. 2000; Arlinghas and Mehner 2003). While there are some examples of copled social-ecological models that link complex angler behavior and fish poplation dynamics (e.g., Cole and Ward 1994; Woodward and Griffin 2003; Massey et al. 2006), to or knowledge only McConnell and Stinen (1979) and Anderson (1993) considered heterogeneity either in angler preferences or fishing practices in a bioeconomic modelling context. In both cases, the modelling frameworks differed sbstantially from that presented here. In particlar, these earlier stdies did not se random-tility models to predict angler participation nder different management scenarios, and the complexity of the biological and anglerbehavior components were mch more simplified. 5

7 Or goals of this stdy are forfold. First, we present an integrative bioeconomic modelling approach that links the ecological, socioeconomic and management components driving angler-effort dynamics to a fish poplation model, and that allowed optimal harvest reglations for varios angler types to be predicted. Second, we demonstrate the importance of assmptions abot angler-effort dynamics in fisheries management by contrasting predictions from models that make traditional assmptions of static or exclsively catch-based dynamic angler behavior with models that assme more complex, mlti-attribte dynamic behavior. In this stdy, complexity in angler behavior is characterized by whether angler-effort dynamics rely on a single fishery attribte to drive angler behavior or on mltiple fishery attribtes. Third, by incorporating heterogeneity in angler behavior into a bioeconomic modelling framework by acconting for the perceived tility a fishery provides to an angler poplation,, we examine how angler diversity (i.e., heterogeneity of angler types) and the composition of the angler poplation (in terms of these angler types) inflence predictions abot optimal management strategies. Finally, we explore how different management objectives, represented by different measres of social welfare, alter predicted optimal management reglations. Rather than simlating a particlar fishery, or approach is stylized in natre and is intended to demonstrate the sitability of an integrated bioeconomic modelling approach for investigating copled angler-fish poplation dynamics. Methods We developed an integrated model in which angler-type-specific tility derived from both catch- and non-catch-related attribtes of the fishing experience was linked to a deterministic age-strctred fish poplation model for a singlespecies, single-lake fishery. Or modelling framework had three components: (i) a 6

8 management component that described the reglations applied to the fishery system, (ii) a socioeconomic component that described the effort dynamics of different angler types, and (iii) a biological component that described the fish poplation dynamics. Angler tility was sed to determine changes in angling effort in the dynamic anglerbehavior scenarios, and to make predictions abot optimal harvest reglations. The reslting impacts on the fish poplation nder different management policies were investigated to determine whether management for social optima also conserved the fish poplation. All model eqations are smmarized in Table 1 and illstrated in Figre 1; model parameters are listed in Tables 2 and 3. Management component Traditional harvest-control measres have focsed on reglating the harvest rates of individal anglers to achieve biological sstainability (Radomski et al. 2001). However, in open-access systems, which are typical for many recreational fisheries (Post et al. 2002), otpt-control measres that do not directly limit angler nmbers cannot constrain total fishing mortality (Radomski et al. 2001; Cox and Walters 2002a; Cox and Walters 2002b). The failre of traditional otpt-control measres to preserve some recreationally exploited fish poplations (Post et al. 2002) has led to a call for inpt-control measres that more directly limit angling effort (Cox and Walters 2002a; Cox and Walters 2002b). Therefore, we investigated two types of reglatory policies over a range of vales (Table 2): a traditional otpt-control reglation, expressed in terms of a minimm-size limit, and an inpt-control reglation, expressed in terms of the nmber of angling licenses issed. Socioeconomic component Angler tility Insert Figre 1 7

9 Economic tility theory assmes that hman agents make choices that will maximize their personal tility (alternatively termed benefits or satisfaction; Perman et al. 2003). For example, from a set of potential alternatives, recreational anglers will choose to fish a fishery that provides them with the greatest possible tility (Hnt 2005). Mltiple attribtes contribte to an individal angler s tility fnction, and the relative importance of fishery attribtes (sch as fish size or crowding), called partworth tilities, for total angler tility vary sbstantially among different angler types (Aas et al. 2000; Oh et al. 2005a; Oh and Ditton 2006). Choice models based on random-tility theory (McFadden 1974; Manski 1977) can be calibrated with actal (revealed) or hypothetical (stated) empirical site-choice data. Sch models constitte one approach that can be sed to predict recreational-angler behavior, which can then be sed to predict and nderstand how anglers will react to changes in the attribtes of a fishery (Palrd and Laitila 2004; Massey et al. 2006; Wallmo and Gentner 2008). Three scenarios of angler behavior were investigated. In the first scenario, we simlated static angler behavior, characterized by anglers that did not respond to changes in a fishery s attribtes (sch as fish size, catch rate or congestion level), bt instead, participated at the maximm effort level allowed. Predictive recreationalfisheries models often assme constant exploitation rates and ignore angler dynamics when evalating reglation impacts (e.g., Dnning et al. 1982). The static scenario mimics this sitation by keeping angling effort constant. In or two other scenarios, anglers were allowed to behave dynamically, i.e., they chose to fish or not to fish depending on the time-varying tility provided by the fishery. Utility fnctions that described the preferences of a particlar angler type for the fishing attribtes experienced were sed to simlate angler-type-specific behavioral decisions. In the second scenario, the tility of fishing was based on the tility gained from catch rates 8

10 alone (Table 1, eqation 1a; and Table 3), an approach sed in previos recreationalfishing models (Cox et al. 2003; Post et al. 2003). In the third scenario, tility was based on a more realistic mlti-attribte tility fnction (Table 1, eqation 1b; and Table 3). Attribtes inclded in this tility fnction were catch rates, average size of fish caght, maximm size of fish caght, angler congestion, minimm-size limit reglations and license costs, all of which have been shown to affect anglers fishing decisions abot participating in a particlar fishery (Hnt 2005). Althogh the mltiattribte tility fnction was not sed to determine angling effort in the static scenario, for comparative prposes it was sed to evalate the qality of the fishery at the end of the simlations (Table 1, eqation 1b) (Figre 1). Angler-effort dynamics In or second and third scenarios, anglers responded dynamically to their perception of fishery qality by changing the amont of effort they devoted to the fishery. In these scenarios, the tility gained from a fishing experience determined the angler s probability of an angler choosing to fish over the alternative of not fishing (Table 1, eqation 2a). This probability was calclated as is typical in empirical choice models (Oh et al. 2005b; Massey et al. 2006). The probability of fishing based on angler tility, as well as the maximm time anglers wold fish in a year irrespective of fishing qality, were then sed to determine realized annal effort of anglers (i.e., the amont of time they actally fished; Table 1, eqations 2b-2e; Figre 1). To accont for the fact that anglers make decisions based on previos experiences and habits, and not exclsively based on their most recent experiences (Adamowicz et al. 1994), a fishing-behavior persistence term (Table 2) was introdced to the effort dynamics (Table 1, eqation 2b). This term described the relative inflence of last year s realized fishing probability on the crrent year s realized fishing probability. Insert Table 1 9

11 We assmed that the realized annal angling effort (Table 1, eqation 2e) was limited by three factors: the realized probability of fishing, the desired maximm effort that an individal angler wold fish irrespective of angling qality (Table 1, eqation 2c), and the inpt-control measre expressed in terms of the nmber of angling licenses issed (Table 1, eqation 2d). The instantaneos fishing effort of a given angler type was assmed to be constant throghot the fishing season, and to eqal zero after the fishing season ended (Table 1, eqation 2f). Angler heterogeneity Angler heterogeneity was introdced into or model by defining three different angler types generic, consmptive, and trophy anglers that differed in their degree of angling specialization (Bryan 1977; Ditton et al. 1992; Table 3). Or parameterization of angler behavior was based on recreational specialization theory (Bryan 1977; Ditton et al. 1992). Bryan (1977) described for general angler types ranging from the casally involved to the techniqe- and setting-specialist. As specialization levels increase, skill levels improve, fish size is of greater importance, and harvesting fish is of lesser importance (Bryan 1977). This can lead to differing propensities to perform volntary catch-and-release (Arlinghas 2007), and to an increased ability to catch more and larger fish (Dorow et al. 2010). Angler preferences also change with specialization: for example the vale of solitde relative to the social aspects of the fishing experience varies with specialization (Ditton et al. 1992; Connelly et al. 2001). Based on pioneering work by Bryan (1977) and sbseqent applications and refinements (e.g., Qinn 1992; Allen and Miranda 1996; Fisher 1997) we devised qalitatively realistic angler-type-specific part-worth-tility fnctions for the varios attribtes of the fishing experience. Figre 2 illstrates Insert Table 2 10

12 qalitative differences in preferences and tolerances for different fishery attribtes among angler types, while Figre 3 illstrates the resltant tility fnctions. Parameters for three stylized angler types were chosen to reflect differential skill, consmptive orientation and overall dedication to the recreational fishing experience (Table 3). Angler types differed in both their fishing practices, and their preferences for varios attribtes of the fishing experience (Figre 2; Table 3). Generic anglers were assmed to be the least specialized, consmptive anglers were intermediate, and trophy anglers were the most specialized. By definition, consmptive anglers had the greatest consmptive orientation. Accordingly, generic anglers were assmed to (i) be least likely to participate in angling activities, (ii) be intermediate in their tolerance of restrictive minimm-size limits, (iii) be the most affected by license costs, (iv) have an intermediate interest in catch rates and be least interested in the challenge of catching fish, (v) be least interested in average fish size and be intermediately interested in trophy-sized fish, (vi) be most tolerant of angler crowding, (vii) be least skilled, and to (viii) practice some volntary catch-and-release of harvestable fish (Table 3). In contrast, consmptive anglers were assmed to (i) participate at an intermediate level in angling activities, (ii) be least tolerant of restrictive minimm-size limits, (iii) be intermediately affected by license costs, (iv) be most interested in catch rates and intermediately interested in the challenge of catching fish, (v) be intermediately interested in average fish size and least interested in trophy-sized fish, (vi) be intermediately tolerant of angler crowding, (vii) have intermediate skills, and (viii) practice no volntary catch-and-release of harvestable fish (Table 3). Finally, trophy anglers were assmed to (i) participate the most in angling activities, (ii) be most tolerant of restrictive minimm-size limits, (iii) be least affected by license costs, (iv) be least interested in catch rates bt most interested in Insert Figre 2 11

13 the challenge of catching fish, (v) be most interested in average fish size and trophysized fish, (vi) be least tolerant of angler crowding, (vii) have the greatest skills, and (viii) practice the most volntary catch-and-release of harvestable fish (Table 3). Trophy anglers were also assmed to target larger fish relative to consmptive and generic anglers (throgh the se of different fishing gear; Rapp et al. 2008; Table 3). Parameter vales and frther jstification for these assmptions are otlined in Table 3, and the reslting shapes of the angler-type-specific part-worth-tility fnctions are illstrated in Figre 3. Althogh these fnctions might look different for particlar fisheries, we believe that their general featres adeqately reflect the angling behavior and preferences of differently specialized recreational anglers. The importance of angler heterogeneity for determining optimal fishing reglations was examined by first comparing model reslts among different homogeneos angler poplations, each composed of a single angler type. However, becase natral angler poplations are likely comprised of a mixtre of angler types, we also considered a mixed angler poplation composed of all three angler types mentioned above. As this aspect increases the model complexity and in an attempt to simplify angler descriptions, recreational-fisheries researchers and managers may wish to simplify angler descriptions by assming some form of average angler behavior (Hahn 1991; Aas and Ditton 1998). Therefore, to examine the importance of explicitly acconting for the composition of the angler poplation on model predictions of optimal reglations, we compare model reslts for an average angler type poplation with those for a corresponding mixed angler poplation composed of three angler types. here, the average angler type was defined by a weighted average of fishing preferences and fishing practices of the three angler types according to their relative freqencies in the mixed angler poplation (Table 2). It shold be noted, that Insert Figre 3 and Table 3 12

14 this is a weighted average and therefore depends on the assmptions abot the relative abndance of angler types in the mixed angler poplation. However, this example demonstrates the implications of the simplifying assmption of an average angler. Biological component Or stdy aimed to show how the biological and socioeconomic and management components of recreational-fishery systems cold be linked in an integrated modelling framework. For brevity we therefore only describe the essentials of the biological component in terms of growth, reprodction and srvival fnctions.tables 1 and 2 provide frther details abot eqations and parameters.. In short, an age-strctred model was sed to describe the fish poplation being exploited. Individal fish within an age class were assmed to be ecologically eqivalent (Tables 1, eqations 3a and 3b). The fish poplation model was parameterized to be representative of a northern pike (Esox lcis L.) poplation. We chose this species de to its importance for recreational fisheries in both North America and Erasia (Pakert et al. 2001; Arlinghas and Mehner 2004a). In all scenarios, the fish poplation reached its demographic eqilibrim prior to the introdction of fishing, and the reslts presented correspond to eqilibrim conditions after fishing was introdced (i.e., we investigated long-term dynamics). The determination of fishing effort (Table 1, eqations 2a-2f) and fish reprodction (Table 1, eqations 5a-5d) were assmed to occr on an annal basis at the beginning of each year, and poplation and fishery characteristics were pdated annally. However, becase recreational fishing is often a size-selective process (Lewin et al. 2006) occrring throghot the year, we described fish mortality and the growth in body size of fish by continos fnctions (Table 1, eqations 4a-4e). This allowed or model to accont for fish to grow into vlnerable size classes within each 13

15 year, and for the recaptre and repeated exposre to hooking mortality of released individals throghot the fishing season, both of which are important aspects of recreational fisheries (Coggins et al. 2007). These resltant ordinary differential eqations were solved nmerically sing the ODE45 fnction in Matlab (version Mathworks, Inc.). Two crcial density-dependent relationships were inclded to allow for compensatory responses of the fish poplation to exploitation (Lorenzen and Enberg 2002): density-dependent biphasic growth in body size (Table 1, eqations 4a-4d) (Lester et al. 2004; Dnlop et al. 2007) and density-dependent srvival from spawning to post-hatch of fish of age zero. The latter was represented by a Beverton-Holt type relationship, which was assmed to apply at the beginning of each year (Table 1, eqations 5c) (Lorenzen 2008). Fish yonger than one year were assmed to experience no frther natral mortality (Table 2) bt cold experience fishing mortality if they became large enogh. Fish one year and older experienced a constant natral mortality rate in addition to size-dependent fishing mortality (Table 2, eqation 7h). Fishing mortality was assmed to be size-dependent in two ways that qantitatively differed among angler types (see Table 3 for angler specific parameters). First, catch rates were dependent on the size-dependent vlnerability of fish to the specific fishing gear tilized by each angler type. Vlnerability to captre therefore differed among age classes and also changed over the corse of the growing season (Table 1, eqations 7a and 7b; see Table 3 for parameters). Catch rates were also dependent on fishing effort and the skill level of the anglers (Table 1, eqation 7b, see Table 3 for parameters). Second, harvest of fish was reglated by a minimmsize limit ( MSL ;Table 1, eqation 7c). While all fish above the legal MSL were 14

16 harvestable, a portion of ndersized fish were also considered harvestable becase of non-compliance with reglations (either throgh ignorance or choice; Sllivan 2002). Anglers chose to harvest fish based on their catch rates mediated by their propensity to volntarily release fish (Table 1, eqation 7e) determined by the personal limit an angler had on the nmber of fish they harvested in a day; (see Table 3 for angler-typespecific parameters). Released fish were assmed to experience hooking mortality from handling or injries (Table 1, eqation 7f; Table 3; Arlinghas et al. 2007, Arlinghas et al. 2008c). Fish nder the legal size limit, which were not part of the pool of illegally harvestable fish, only experienced hooking mortality (Table 1, eqation 7g). After fishing was introdced, the fish poplation was allowed to eqilibrate. The spawning potential ratio ( SPR ) was sed to assess the biological impacts of angling exploitation. SPR, which has previosly been sed in recreational-fishing models (Coggins et al. 2007; Allen et al. 2009), measres redctions in the fish stock s reprodctive otpt, and can ths serve as an indicator of recritment overfishing (Goodyear 1993; Coggins et al. 2007; Allen et al. 2009). In or model, we se a weighted SPR (Table 1, eqation s 5b and 6). Depending on the life history of a species, vales below are considered critically low (Goodyear 1993) and it is commonly assmed that SPR shold be maintained above to redce the risk of recritment failre (Goodyear 1993; Coggins et al. 2007). We sed these vales as criterion to assess the risk of recritment overfishing nder different management policies. Social-welfare measres Social welfare was sed to determine optimal reglations. Social welfare is an aggregation of individal tilities (Perman et al. 2003) and determines the total 15

17 economic vale of a good or service, sch as a recreational-fishing experience, as perceived by anglers (Edwards 1991). A social welfare fnction describes how individal tilities are aggregated based on their social worth, and it is assmed that any concerns abot eqity are acconted for in the aggregation method (Perman et al. 2003). However, maximizing social welfare does not necessarily reslt in an eqitable distribtion of resorces among individals, nor is there niversal consenss on what constittes an appropriate social-welfare measre or fnction (Perman et al. 2003). Managers mst therefore careflly decide what social-welfare measres reflect their management objectives (e.g., maximizing angler satisfaction and/or participation). In most model simlations described below, a tilitarian social-welfare fnction was sed, referred to as total tility (TU), in which individal tilities were weighted eqally among angler types. However, in a sbset of simlations, three different social welfare fnctions, representing different management objectives, were sed to examine how these differences alter predictions abot socially optimal management reglations. The first welfare measre, TU, described the tility gained by an angler type per fishing experience, mltiplied by the total annal nmber of fishing experiences (measred in terms of angling effort, and expressed in angling days) by that angler type, and smmed over all angler types (Table 1, eqation 8a; similar to McConnell and Stinen 1979). TU reflects the realized demand for angling experiences. However, TU may be inflenced heavily by individals with disproportionately large tility, and a more eqitable distribtion of resorces among all anglers in the angler poplation may be desired (Loomis and Ditton 1993). Ths, a second, more eqitable tilitarian social-welfare fnction (EU) was examined. Here, individal tility from a fishing experience was weighted by the relative abndance of angler types in the angler poplation, to create a weighted mean tility for an 16

18 individal, which was then mltiplied by the aggregate nmber of angling days (Table 1, eqation 8b). Finally, we examined a Rawlsian approach (RU) to tility maximization, where the tility of the worst-off individal was maximized, emphasizing the objective of achieving the most eqitable distribtion of resorces (Perman et al. 2003). Here, the tility from the angler type with the lowest individal tility was sed and mltiplied by the aggregate nmber of angling days (Table 1, eqation 8c). Natrally, the second and third social-welfare measres only differed from the first measre in the mixed angler poplation composed of different angler types. Otline of analysis Across a range of minimm-size limits and angling-license nmbers, three different angler-behavior scenarios static, catch-based dynamic and mlti-attribte dynamic scenarios were considered for five different types of angler poplations generic, consmptive, trophy, average, and mixed. Optimal inpt and otpt reglations were identified by maximizing one of three measres of social welfare total tility TU, eqitable tilitarian tility EU, and Rawlsian tility RU (Table 1, eqations 8a-c). With this approach, we examined the impacts of dynamic angler behavior, angler heterogeneity, and composition of the angler poplation on socially optimal reglations and the reslting biological impacts on the fish poplation. In most analyses presented, TU was sed to determine socially optimal management reglations. However, we also examined the EU and RU social-welfare measres in the context of mlti-attribte dynamic angler behavior and mixed angler poplations, to demonstrate how different management objectives alter socially optimal management reglations. 17

19 We sed sensitivity analyses to explore the importance of different attribtes for determining angler behavior, optimal reglations and biological impacts, by removing in trn each attribte from the mlti-attribte angler-behavior scenario. However, given the hypothetical natre of the constrcted angler types and their partworth-tility fnctions (Figre 3), we decided it wold be imprdent to derive generalized conclsions abot the relative importance of individal attribtes in determining optimal reglations. Therefore, sensitivity analyses were not intensified beyond the approach smmarized above. Reslts Impacts of dynamic angler behavior A comparison of the three angler-behavior scenarios showed sbstantial differences in predictions of total tility (left to right in Figre 4). Optimal minimmsize limits were predicted to be highest in scenarios with catch-based dynamic angler behavior and were generally lower (and similar) for corresponding scenarios with static and mlti-attribte dynamic angler behavior for angler poplations composed of one angler type (Table 4; Figre 4). Optimal effort reglations were lowest in the static scenarios, intermediate in the mlti-attribte scenarios, and highest in the catchbased scenarios (Table 4). In fact, optimal license nmbers in the catch-based scenarios were often more than two times larger than the nmber predicted in the other scenarios. Under predicted optimal reglations, the nmber of hors that anglers actally fished, termed realized angling effort, were identical in the static and mltiattribte scenarios when the angling poplation was composed of one angler type, (ths following the pattern of predictions for optimal minimm-size limits). In the catch-based scenario, realized effort followed a trend similar to that of optimal license nmbers. Insert Figre 4 and Table 4 18

20 The risk of recritment overfishing and the biological impacts of recreational angling on the modelled pike poplation were affected by the type of angler behavior considered (Figre 5). Static angler behavior cased the most negative impacts on the fish poplation across the range of minimm-size limits and license nmbers examined, compared to the two scenarios in which anglers behaved dynamically. This was becase realized angling effort in the static angler-behavior scenario was fixed at the maximm level allowed, whereas in the two dynamic scenarios realized angling effort was less and depended on the tility anglers gained from the fishery. When comparing the two dynamic scenarios, biological impacts of fishing at low to moderate MSL levels in the catch-based scenario were generally less severe than in the mlti-attribte scenario, with the latter approaching recritment overfishing and fishery collapse at lower license nmbers. At high MSL levels, approaching complete catch-and-release conditions, the risk of recritment overfishing was often greater in the catch-based scenario, althogh the SPR never dropped below 0.4, even when a large nmber of licenses were issed. Impacts of angler heterogeneity Not only angler dynamics, bt also angler heterogeneity sbstantially affected model-predicted optimal inpt and otpt reglations. When the three angler types were compared (first three rows in Figre 4), optimal minimm-size limits were generally intermediate for generic anglers, low for consmptive anglers and high for trophy anglers, with the latter approaching complete catch-and-release conditions, except in the catch-based scenario, in which complete catch-and-release reglations were preferred by all angler types (Figre 4; Table 4). Optimal effort reglations were fond to be the lowest for consmptive anglers in the static and mlti-attribte scenarios, intermediate for trophy anglers and highest for generic anglers. However, Insert Figre 5 19

21 in the catch-based scenario, all angler types preferred a large nmber of licenses, with generic anglers favoring somewhat fewer angler licenses than the other angler types. Under optimal reglations, consmptive anglers were predicted to fish the least, bt generic and trophy anglers invested more (and similar) realized angling efforts in the static and mlti-attribte scenarios (Table 4). However, in the catch-based scenario, consmptive anglers invested the most realized angling effort. At their optimm, trophy anglers, as a homogeneos grop, derived the highest tility from fishing, exceeding that of the other anglers types by a factor of more than two; generic anglers were intermediate, while consmptive anglers derived the least tility in the static and mlti-attribte scenarios (Figre 4). Differences among the angler types also affected the risk of recritment overfishing. In all scenarios and across all reglation combinations, consmptive anglers generally had the most negative impact and generic anglers the least, except in the mlti-attribte scenario at high MSL levels. This trend was also seen when examining the biological impacts of different angler types nder the different reglations they perceived as optimal (Table 4). Under these optimal reglations, the biological impact of consmptive anglers was greatest, occrring close to the threshold levels of recritment overfishing ( ) and at reglation combinations for which small changes in reglations cold case large changes in the risk of recritment overfishing (Figre 5). At these respective optima, generic and trophy anglers impacted the fish poplation mch less than consmptive anglers and at reglation combination that imply a low risk of recritment overfishing. We fond the sensitivity of reslts to individal attribtes in the mlti-attribte scenario varied in their effect on optimal reglations, realized effort and SPR, and varied greatly with angler type, withot any consistent pattern becoming evident 20

22 (Table A1). We cold tentatively conclde, however, that findings for trophy anglers were strongly dependent on crowding aversion, while findings for consmptive anglers were particlarly sensitive to MSL levels and some catch attribtes. It was also interesting to notice that the response of mixed angler poplations to the removal of a particlar fishery attribte sometimes exceeded that of homogeneos angler poplations, highlighting the importance of inclding heterogeneity in angler preferences (Table A1). Impacts of angler-poplation composition Predictions of optimal inpt and otpt reglations sbstantially differed between the average angler and the mixed angler poplation (bottom two rows in Figre 4). Under optimal reglations, license nmbers and realized angling efforts were higher for the mixed angler poplation than for the average angler poplation (Table 4). Optimal MSL levels for the mixed angler poplation were the same as the average angler poplation in the static scenario, lower in the catch-based scenario and higher in the mlti-attribte scenario. In addition, across all scenarios, TU nder optimal reglations was greater in the mixed angler poplation than in the average angler poplation. For the average angler poplation was assmed, minimm-size limits and realized efforts nder optimal reglations were identical in the static and mltiattribte scenarios. However, for the mixed angler poplation, minimm-size limits, license nmbers and realized efforts nder optimal reglations were sbstantially higher in the mlti-attribte scenario than in the static scenario (Figre 4; Table 4). Frthermore, in the mlti-attribte scenario, predictions of optimal license sales and realized efforts were generally higher than in any of the three homogeneos angler poplations (Table 4). The mixed angler poplation was also predicted to have a 21

23 greater biological impact than the average angler poplation (Figre 5). However, nder optimal reglations, the risk of recritment overfishing in both cases was low (Table 4). Changes in the composition of the mixed angler poplation that fished in the mlti-attribte scenario were described by the changes in the proportion total realized angling effort invested by each angler type (Figre 6). This shows that the composition of the angling poplation varied depending on minimm-size limits and license reglations, with trends predominantly following changes in MSL (Figre 6). At low MSL levels and low license nmbers, all angler types fished in approximately eqal proportions, whereas at low MSL levels and high license nmbers the composition of the angling poplation resembled that of the entire angler poplation (i.e., 40% generic, 30% consmptive and 30% trophy). At moderate to high MSL levels the majority of consmptive anglers in the angler poplation chose not to fish, and ths dropped ot of the angling poplation. Even higher MSL levels reslted in generic anglers dropping ot too, and ths in an angling poplation dominated by trophy anglers. Under optimal reglations, the composition of the angling poplation in the mlti-attribte scenario was heavily skewed toward generic and trophy anglers, with few consmptive anglers being attracted to the fishery (Table 4; Figre 6). Impacts of social-welfare measres In the mlti-attribte scenario for the mixed angler poplation, socially optimal minimm-size limits were highest for total tility (TU), intermediate for eqitable tilitarian tility (EU) and lowest for Rawlsian tility (RU) (Figre 7; Table 4). Optimal license nmbers were also highest for the TU social-welfare measre, bt lower (and similar) for the EU and the RU social-welfare measres, and realized angling efforts nder optimal conditions showed the same pattern. Insert Figre 6 22

24 Under optimal reglations, optimal license nmbers and realized angling efforts for the average angler poplation never exceeded those for the mixed angler poplation, irrespective of the applied social-welfare measre (Table 4). However, the optimal MSL was slightly higher in the average angler poplation than in the mixed poplation when a RU social-welfare measre was applied (Table 4). Under optimal reglations, SPR levels were well above 0.40, irrespective of the applied socialwelfare measre (Table 4); therefore, all social-welfare measres avoided recritment overfishing nder optimal reglations. Discssion We developed a bioeconomic modelling approach that integrates angler behavior and angler heterogeneity with age-strctred and density-dependent fish poplation dynamics, to determine socially optimal inpt and otpt reglations for a recreational fishery. Using this approach, we have demonstrated how angler behavior and heterogeneity affect optimal reglations, and how optimal reglations varied with the social-welfare measre applied. Angler behavior The importance of acconting for angler behavior was demonstrated by the differences observed in predicted optimal reglations (expressed in terms of minimm-size limits and license nmbers) among three angler-behavior scenarios that describe, respectively, static, catch-based dynamic and mlti-attribte angling dynamics. Predicted optimal minimm-size limits and license nmbers were sbstantially higher for the catch-based scenario than for the other two scenarios. However, most pblished recreational-fisheries models that incorporated dynamic angler behavior assmed that anglers respond to catch rates alone or some measre of fish abndance (Johnson and Carpenter 1994; Beard et al. 2003; Post et al. 2003), Insert Figre 7 23

25 ths neglecting other attribtes known to affect participation decisions of anglers (Hnt 2005). Or findings call into qestion the validity of this simplifying assmption and reslting predictions of optimal reglations. For example, when catch rate was assmed to be the only attribte determining the fishing decisions of anglers, the catch-based scenario predicted optimal inpt and otpt reglations that effectively imply complete catch-and-release reglatory policies at largely nlimited effort levels. This prediction is clearly misleading in many sitations and reslts from an oversimplification of angler preferences. Indeed, becase some angler types are strongly harvest-oriented, management conflicts and dilemmas have occrred in some recreational fisheries despite high catch rates, when the possibility for anglers to harvest was constrained (Matlock et al. 1988; Radomski 2003; Sllivan 2003). Perceived harvest constraints may reslt in the displacement of harvest-oriented anglers to alternative fisheries (Radomski and Goeman 1996; Beard et al. 2003), an important effect that cannot be captred by models that assme angler behavior to be driven by catch rates alone. In contrast, or investigations of mlti-attribte dynamic angler behavior, presmably allowing a more realistic representation of angling effort, showed that complete catch-and-release reglations were not always socially optimal. Or sensitivity analyses highlighted that, while most attribtes of the fishing experience (sch as fish size, catch rate, crowding, aversion to reglations, etc.) were important for determining angler choice and angler welfare, their relative importance varied among angler types (Table A1). This nderscores the importance of inclding all relevant catch- and non-catch-related attribtes affecting angler choice in 24

26 bioeconomic fisheries models to more accrately predict angler behavior and fishing pressre, and to derive optimal reglations that maximize angler welfare. A mlti-attribte perspective on angler behavior and welfare is also likely to improve predictions of the biological impacts of fishing nder different reglations. Historically, angler poplations were expected to be self-reglating, as anglers were assmed to leave a fishery when catch rates declined (Cox and Walters 2002a, Radomski 2003). However, becase catch rate is jst one among many attribtes characterizing a fishing experience, sch catch-based self-reglation does not necessarily apply (Post et al. 2002; Palrd and Laitila 2004; Post et al. 2008). Indeed, we fond that realized angling effort and the biological impacts were higher in the mlti-attribte scenario than in the catch-based scenario at low to intermediate MSL levels. These finding corroborate claims that mlti-attribte angler behavior may pt fish poplations at risk of overexploitation (Post et al. 2002), since anglers contine to be attracted to particlar fisheries even after catch rates have declined becase other attribtes of the fishery (sch as close proximity, social aspects of the experience) provide them with tility, and thereby partly compensate for redced catch rates. The interesting featres of the mlti-attribte tility scenario derive from its partial decopling of fish and angler dynamics (Johnson and Carpenter 1994). In contrast, the catch-based scenario is appropriate for describing predator-prey interactions where a predator s fitness is predominantly dependent on prey consmption. Not acconting for the array of attribtes that attract anglers to a fishery may therefore lead to an nderestimation of the biological impacts of fishing (Post et al. 2002). Conseqently, management decisions based on assmptions of prely catch-based angler behavior will likely be less conservative than intended with regard to limiting 25

27 biological impacts, and probably also less sccessfl than intended with regard to angler satisfaction and participation. Angler heterogeneity Or reslts have shown that acconting for the complexity of angler behavior when predicting the amont of angling effort invested in a particlarly fishery can fndamentally improve predictions abot optimal reglations. However, this improvement alone might not be enogh: predictions are likely even more realistic when the heterogeneity of angler behavior is considered in recreational-fisheries models. We fond that, becase of the consmptive orientation and aversion to angling reglations of some angler types, minimm-size limits were particlarly important in determining angler tility and optimal reglations. Under less restrictive otpt reglations, consmptive angling effort was redced, becase the fish poplation cold not spport large nmbers of harvest-oriented anglers while at the same time maintain high catch rates. In these sitations, trophy anglers fished in greater nmbers than consmptive anglers, becase they were less concerned with harvest constraints and more interested in attribtes of the fishery nrelated to catch rates. Despite their greater nmbers, at low MSL levels the less consmptive natre and the redced catch rates of trophy anglers (which occrred becase they sed gear that targeted fish of larger size) reslted in them imposing less fishing mortality on a fish stock than consmptive anglers. This demonstrates that both aspects of angler heterogeneity, diversity in angling preferences and differences in fishing practices, are important when determining optimal angling reglations. Frthermore, while managing for angler diversity to enhance the recreational fishing experience of all anglers has been 26

28 repeatedly called for (Driver et al. 1984; Aas et al. 2000; Arlinghas and Mehner 2004a), or stdy is the first to explicitly demonstrate the benefits of sch an approach when determining optimal, angler-type-specific reglations to maximize social welfare. Althogh the aim of or modelling exercise was to explore the general importance of behavioral complexity and diversity in anglers, or model-based reslts also highlight some practical implications. In particlar, or model findings sggest that some MSL reglations crrently sed for pike fisheries (45-75 cm in North America; Pakert et al. 2001) are below the optimal levels (53-99 cm) predicted by or model for the different angler types. Implementation of lower-than-optimal minimm size limits cold pt fish poplations at risk of recritment overfishing. Ths, depending on the composition of the local angler poplation, special reglations described by Pakert et al. (2001) that are geared toward particlar angler types (e.g., maximm-size limits, inverse slot length limits) may perform better than the standard soltion of imposing a moderately low minimm-size limit (sch as cm). Despite considerable differences among angler types, we fond that socially optimal reglations reslted in biologically sstainable exploitation patterns. This is becase angler tility is partly dependent on catch-related attribtes of the fishery (sch as catch rates or fish size), which implicitly reqires a prodctive, biologically sstainable fishery in the long term. Or reslts therefore indicate that socioeconomic management objectives, sch as maximizing social welfare, can accont for the state of a fish poplation throgh its inflence on angler tility and ths provide management advice that reslts in biologically sstainable exploitation. This spports sggestions for a focs on optimal social yield (OSY) when managing for sstainability (Roedel 1975; Malvestto and Hdgins 1996; Carpenter and Brock 27

29 ). However, the occrrence of optimal reglations in the vicinity of SPR levels sggestive of recritment overfishing varied with angler type. Ths, a precationary approach has to be taken in socially optimal management, to accont for the stochastic processes nderlying any fishery. Angler poplation composition The reslts discssed so far accont for the dynamics and heterogeneity in angler behavior, they are still limited, in the sense that the angler poplation was assmed to be composed of jst one angler type. In reality, angler poplations are composed of different types of anglers that vary in their preferences and behavior (Hahn 1991; Fisher 1997; Connelly et al. 2001). Or stdy has shown that this composition affects optimal reglations. Moreover, while, managers might be inclined, for the sake of simplicity, to represent angler poplations in terms of an average angler (Hahn 1991; Aas and Ditton 1998), we fond that sch a simplification can lead to misleading predictions of optimal reglations and biological impacts. This is becase different angler types dominated the realized angling effort nder different reglations, and becase optimal reglations were consistently more restrictive for the mixed angler poplations than for the average poplations. Shifts in the angling poplation was also important for determining biological impacts, becase of differences in fishing practices and participation of the different angler types. Therefore, or model reslts nderscore the importance of considering not only dynamic angler behavior and angler heterogeneity in both angling preferences and angling practices in models of recreational-fisheries management (Post et al. 2008), bt also how dynamics and diversity interact in angler poplations containing a mixtre of angler types. Or findings sggest that crrent monitoring methods that pool information abot anglers need to be modified to accont for the heterogeneity 28

30 of angler types sing specific fisheries. This will allow managers to nderstand better which types of anglers are fishing and why (Radomski et al. 2001), ths yielding insights that or model reslts sggest cold be of crcial importance for determining optimal reglations and for more accrately predicting the biological impacts of the angling poplation. Social-welfare measres A final insight from this stdy relates to the importance of the management objectives determining optimal inpt and otpt reglations. From a welfareeconomics perspective, the management objective is to maximize the social welfare a fishery provides to the angling commnity irrespective of which anglers benefit the most or the least (Cole and Ward 1994; Perman et al. 2003). However, or reslts sggest, that a strictly tilitarian economic approach may alienate some angling grops from a fishery that is managed for maximm total tility. For example, we fond that consmptive anglers interested in fish harvest were no longer attracted to a fishery that was sbject to restrictive maximm-size limits. Trophy anglers, in contrast, enjoyed high individal tility at high MSL levels, mainly becase of their lack of consmptive orientation and the greater importance of fishing to their lifestyle. As a reslt, trophy anglers gained more tility, which strongly inflenced the TU social-welfare measre, and ths optimal reglations. Social-welfare measres that reflected more eqitable management objectives, sch as eqitable tilitarian tility (EU) or Rawlsian tility (RU), rendered optimal reglations in mixed angler poplations more restrictive, bt reslted in a more diverse composition of anglers attracted to a fishery. Ths, althogh there is no niversal consenss abot which social-welfare fnctions to se to qantify welfare (Cole and Ward 1994; Perman et al. 2003), or 29

31 reslts illstrate how the optimal reglations predicted by bioeconomic models are sensitive to the social-welfare measres applied. Therefore, managers need to be explicit abot their nderlying management goals and objectives (Barber and Taylor 1990; Aas and Ditton 1998), and ensre that the welfare measre applied closely reflects these objectives, when implementing an OSY approach to recreationalfisheries management. Limitations and extensions While we hope that or stdy provides valable insights abot the importance of angler dynamics and angler heterogeneity when managing for OSY, several limitations need to be highlighted. First, or model reslts depend on the description of angler behavior. Application of or modelling approach to local fisheries therefore reqires a qantitative assessment of the local and regional angler poplations, e.g., sing stated and revealed choice models (Hnt 2005; Massey et al. 2006). A second limitation is that we assmed that over time, anglers will follow the same behavioral patterns and will keep occrring in the same proportions, which may be in error (Baerenkla and Provencher 2005). Temporal trends in the behavior of individal anglers or in the composition of the angler poplation cold be examined in ftre extensions of or model. Changing preferences of anglers over time de to specialization or learning, cold also be exciting to investigate, as angler will likely adapt to changes in the fishery by altering their expectations (Arlinghas 2006a). Third, to simplify an already complex, model we assmed that participation decisions were made on an annal basis, whereas other time steps may be more realistic (Schhmann and Schwabe 2004; Hnt 2005). However, becase we were interested in long-term eqilibrim conditions, or simplifying assmption seems warranted. Forth, or model described a single fishery and therefore did not accont 30

32 for changes in tility offered by sbstitte sites in the vicinity of the modeled fishery. Clearly, this is an nrealistic assmption, and frther research is needed to broaden or modelling approach to fisheries landscapes (Lester et al. 2003). A final limitation of this stdy is that we defined social welfare in terms of aggregated tility, rather than aggregated willingness-to-pay. In environmental and resorce economics, inclding recreational-fisheries economics, an aggregate of individals willingness-to-pay for an environmental good or service is a commonly sed welfare measre (Edwards 1991). In empirical stdies of non-marketable goods and services, sch as recreational fisheries, this measre of social welfare is calclated sing the change in tility provided by attribtes of the good (sch as catch rate or crowding) from one condition of the fishery to another divided by the marginal tility of income (sch as the license cost coefficient in or model) and is expressed in monetary nits (Hanemann 1984). Here, we chose not to express tility in monetary nits, becase this wold necessitate making an additional assmption abot the baseline condition sed for comparison, and becase it was felt to be imprdent to pt a monetary vale on hypothetical scenarios. However, sch calclation cold be carried ot if appropriate empirically derived parameters were available from statedor revealed-preference models for angler-type-specific part-worth-tility fnctions (e.g., Massey et al. 2006). This wold also ensre that the welfare measre has a cardinal scale avoiding the potential debate of how comparable tility is among individals (Perman et al. 2003). Despite these limitations, by copling socioeconomic and biological models or modelling framework is among the few that addresses the often-toted need for an interdisciplinary approach to recreational-fisheries management (e.g., Anderson 1993) (Johnson and Carpenter 1994; Radomski et al. 2001), and provides a basis for ftre 31

33 research. There are nmeros directions in which or model can be extended, inclding incorporating environmental stochasticity and a mlti-species biology. These extensions are important becase deterministic models (Carpenter et al. 1994) and single-species models (Worm et al. 2009) may reslt in erroneos conclsions abot appropriate management strategies. In mlti-species models, incorporating angling preferences for different species and indirect effects of angling on the aqatic food webs (Roth et al. 2007) are promising options for complementing the predictions presented here. Frther avenes for ftre research inclde, exploring the part-worth-tility fnctions driving angler behavior, examining the sensitivity of model predictions to changes in fishery attribtes, and investigating an even larger nmbers of prototypical angler types and their interactions in mixed angling poplations Becase mlti-lake fisheries opportnities (Parkinson et al. 2004; Post et al. 2008) are more realistic than the simplified single-lake perspective have adopted here, exploration of angler choice within a landscape of fishing opportnities (Carpenter and Brock 2004) may be the most important extension of or modelling approach. Implications Even thogh we have jst scratched the srface, we hope that readers share or optimism that the interdisciplinary approach to modeling recreational fisheries introdced here constittes a sond and extensible theoretical framework. The approach bilds on choice theory from welfare economics, angler-specialization theory from leisre sciences and traditional ecological theory, and provides niqe insights into recreational-fisheries management. A key finding of this stdy and related work (Carpenter and Brock 2004) is that one-size-fits-all policies are likely to prodce sboptimal management 32

34 otcomes, becase they cannot accont for the diversity and complexity of angler behavior that is inherent to most of the world s recreational fisheries (Cox et al. 2003; Arlinghas et al. 2008a; Post et al. 2008). Frthermore, we have shown that misleading predictions abot optimal management can reslt from the omission of dynamic angler behavior and angler heterogeneity from recreational-fisheries models; this can pt fish poplations at risk of overfishing, in line with what has been sggested by other stdies (Carpenter et al. 1994; Parkinson et al. 2004). In contrast, althogh managers need to be aware that socially optimal reglations strongly depend on the applied measre of social welfare and the management objectives pon which it is based, managing for socially optimal reglations reslted in both social and biological sstainability. Managers are likely to enconter difficlties in jointly satisfying the interests of the entire angling pblic. Decisions therefore need to be made abot how to best distribte access to scarce resorces across angler types (Loomis and Ditton 1993; Daigle et al. 1996). The benefit of an interdisciplinary bioeconomic modelling approach, sch as the one presented here, is that it enables managers to qantify welfare changes reslting from alternative management scenarios, and to predict how these reglations will affect different segments of the angling pblic, as well as the fish poplation. A decision-spport tool sch as this one, bilt on clear objectives and qantitative descriptions, thereby fostering transparency and defensibility in the management process, can facilitate decision taking and clarify when managing for diverse angling opportnities is the best strategy. Ideally, acconting for angler dynamics and angler diversity in fisheries-management models will provide more accrate and realistic predictions of optimal reglations that maximize angler 33

35 satisfaction, minimize conflicts among angling grops and reslt in the sstainable management of recreational fisheries. Acknowledgments We thank Ben Beardmore, Barbara Fischer, Brad Gentner, Wolfgang Haider, Len Hnt, and Shichi Matsmra for advice dring the development of this stdy. We are also indebted to two anonymos reviewers for constrctive comments that helped s improve the clarity of this manscript. Financial spport for this research was provided by the Gottfried-Wilhelm-Leibniz Commnity throgh the Adaptfish Project ( RA received additional fnding throgh the German Ministry for Edcation and Research (BMBF) throgh the Program for Social-Ecological Research (SOEF) within the Besatzfisch-Project (Vorhaben 01UU0907, UD grateflly acknowledges financial spport by the Eropean Commission, throgh the Marie Crie Research Training Network on Fisheries-indced Adaptive Changes in Exploited Stocks (FishACE, MRTN-CT ) and the Specific Targeted Research Project on Fisheries-indced Evoltion (FinE, SSP ) nder the Eropean Commnity s Sixth Framework Program. UD received additional spport by the Eropean Science Fondation, the Astrian Science Fnd, the Astrian Ministry of Science and Research, and the Vienna Science and Technology Fnd. References Aas, Ø., and Kaltenborn, B.P Consmptive orientation of anglers in Engerdal, Norway. Environ. Manage. 19(5): Aas, Ø., and Ditton, R.B Hman dimensions perspective on recreational fisheries management: implications for Erope. In Recreational fisheries: 34

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48 Table 1 Model eqations. The modelled species was pike (Esox lcis L.). Variables, parameters, parameter vales and their sorces are listed in Tables 2. Angler types are specified in Table 3. Nmber Eqation Description Individal-angler tility 1a U fj = U Conditional indirect tility gained by an cj angler of type j from choosing to fish in the catch-based scenario only 1b U = U + U + U + U fj 0j cj sj xj + U + U + U aj rj oj Angler-effort dynamics Conditional indirect tility gained by an angler of type j from choosing to fish in the static and mlti-attribte scenarios 2a p fj = exp( Uˆ fj ) exp( U ) + exp( Uˆ ) n fj Probability that an angler of type j chooses to fish, over the alternative to not fish, where ( U ˆ ) applies to the previos year f j 2b p ˆ Fj (1 ϕ) pfj ϕ pf j = + Realized probability that an angler of type j chooses to fish, where p ˆ F j applies to the 2c Dj pf jdmax 2d AL j L previos year = Nmber of days an angler of type j chooses j to fish dring a year = A ρ Nmber of licensed anglers of type j 2e E = D AL Ψ / φ Total annal realized fishing effort per nit j j j 47

49 area of all anglers of type j 2f e jt Ej / SF if t S = 0 if t > S F F Instantaneos fishing effort per nit area at time t of all anglers of type j Age-strctred fish poplation 3a N total a max = N a= 0 a Total fish poplation density 3b B total a max = NaW a= 0 a Total fish biomass density Growth 4a h = h max 1 + B / B total 1/2 Maximm annal growth of a fish dependent on the biomass density at the beginning of the year 4b p a G 1 (1 + La 0 / h) if a am 1 = 3 + G 1 if a < am 1 Proportion of the growing season dring which a fish of age a allocates energy to growth 4c g at h/ SG if t pas = 0 if t > pas G G Instantaneos growth rate in length of a fish of age a at time t 4d Lat = La 0 + gatt Length of a fish of age a at time t 4e W at = wl Mass of a fish of age a at time t l at Reprodction 5a δwgsi a / We if a am Ra = 0 if a < am Annal fecndity of a female fish of age a 48

50 5b 5c b s 0 max =Φ a RaN a a= am α = 1 + b/ b 1/2 Annal poplation fecndity density, plsed at the beginning of the year Srvival probability from spawning to posthatch of fish of age zero, applied at the beginning of the year 5d N0 = s0b Density of age zero fish at the beginning of 6 SPR bf / bu Mortality the year = Spawning potential ratio (= relative redction in egg prodction nder fishing relative to the corresponding nfished condition) z 7a v = [1 exp( y L )] Proportion of fish of age j a that are ajt j at vlnerable to captre by anglers of type j at time t 7b cajt = qjejtv Instantaneos per capita catch rate of fish of ajt age a by anglers of type j at time t 7c H ajt 1 if Lat MSL = fnj if Lat < MSL Proportion of fish at age a that are harvestable by anglers of type j at time t 7d a max C = c N H jt ajt a ajt a=0 Instantaneos catch rate of harvestable fish by anglers of type j at time t 7e CH jt Cjt cmax jejt = min(, / Ψ ) Instantaneos harvest rate by anglers of type j at time t 49

51 C C C 7f Hjt jt Hjt fhjt = + fhj Cjt Cjt Proportion of vlnerable harvestable fish killed by anglers of type j at time t 7g mf = fh c H + fh c (1 H ) Instantaneos per capita fishing mortality rate ajt jt ajt ajt j ajt ajt of fish of age a imposed by anglers of type j at time t 7h d m m Instantaneos per capita mortality rate of fish at = na + fajt j of age a at time t 7i dn dt a = d N at a Continos rate of change in the density of fish of age a at time t Social-welfare measres 8a 8b 8c U = U D A Annal total tility TU fj j Lj j U ( U ρ ) ( D A ) Annal eqitable tilitarian tility = EU fj j j Lj j j U = min( U ) ( D A ) Annal Rawlsian tility RU fj j L j j j

52 Table 2 Model variables, parameters, parameter vales and their sorces. The modeled species was pike (Esox lcis L.). Eqations are listed in Table 1. Angler types are specified in Table 3. Symbol Description (nit, where applicable) Eqation Vale or range Sorce Index variables j Angler type Generic, consmptive, trophy, or average a Age class (y) 0 - a max a Maximm age of a fish (y) 15 (1) max t Time within the year (y) 0-1 Angling reglations MSL Minimm-size limit (cm) 7c A Nmber of angling licenses (= L 2d Angler poplation nmber of licensed anglers) ρ j Proportion of the angler poplation that is composed of anglers of type j 2d, 8b Non-mixed: 1.0 for one j ; 0.0 for the others Mixed: (0.4, 0.3, 0.3, 0.0) Angler-effort dynamics U n Conditional indirect tility gained by an angler from choosing not to fish 2a 0 51

53 ϕ Persistence of fishing behavior (= 2b 0.5 Ψ the relative inflence of last year s realized fishing probability on the crrent year s realized fishing probability) Average time an angler will fish in a day (h) 2e 4 * D Maximm nmber of days that an max 2c 40 * angler wold fish per year irrespective of fishing qality φ Lake area (ha) 2e 100 S F Annal dration of the fishing season (y) 2f 9/12 Age-strctred fish poplation N Density of fish of age a (ha -1 ) 3a, 3b, 5b, a 0-5d, 7d Growth h Maximm growth increment (cm) 4a 24.0 max B 1/2 Total fish biomass density at which 4a the growth increment if halved (kg -1 ha) G Annal reprodctive investment 4b

54 a Age at first spawning (y) 4b, 5a 2 (4) m L Length of fish of age a at the a0 4b beginning of a year (cm) L Length of fish at hatch (cm) 4b 0.8 (2) 0 S G w l Annal dration of the growing season (y) Scaling constant for length-mass relationship (g cm -l ) Allometric parameter for lengthmass relationship 4c 1.0 4e (6) 4e (6) Reprodction GSI Gonadosomatic index (= gonadic mass/somatic mass) 5a 0.17 (3) W Average egg mass (g) 5a (3) e δ Proportion of eggs that hatch 5a 0.75 (4) Φ α Proportion of female fish in the spawning poplation Maximm proportion of offspring srviving from spawning to posthatch 5b 0.5 (5) 5c b Annal poplation fecndity density 1/2 5c 20,325 at which srvival of offspring from 53

55 spawning to post-hatch is halved (ha) b F Annal poplation fecndity nder fishing b U Mortality Annal poplation fecndity nder nfished conditions m Instantaneos natral mortality rate na of fish of age a (y -1 ) 7h 0.00 if a = if a > 0 (4) Sorces: (1) Craig and Kipling 1983; (2) Frost and Kipling 1967; (3) Hbenova et al. 2007; (4) Kipling and Frost 1970; (5) Le Cren et al. 1977; (6) Willis * Estimated from average participation rates and average lengths of fishing trips obtained from diary data of recreational anglers in Mecklenbrg-Vorpommern, Germany (Dorow and Arlinghas, npblished data) and other literatre (van Poorten and Post 2005; Post et al. 2008). Estimated from empirical length-at-age and biomass density data from varios pike stdies (Kipling and Frost 1970; Kipling 1983a; Tresrer et al. 1992; Pierce et al. 2003; Pierce and Tomcko 2003; Pierce and Tomcko 2005) by minimizing the sm of sqares sing the solver fnction in Excel (Microsoft Office Excel 2003). Estimated from modified data on female biomass and age-2 abndance in Lake Windermere (Kipling 1983b). Egg density was determined sing the relative fecndity relationship reported in (Craig and Kipling 1983) and adlt biomass (Kipling 1983b), and 54

56 natral mortality information from Kipling and Frost (1970) was sed to calclate age-1 abndance from age 2 abndance. 55

57 Table 3 Angler types and their angling behavior. Parameters describe for angler types (generic, consmptive, trophy, and average) in terms of the basic tility they gain from fishing, their tolerances with regard to managerial constraints, their preferences with regard to attribtes of the fishing experience, and their fishing practices. Parameter vales for the average angler type are weighted averages of the corresponding parameter vales for the three prototypical angler types, weighted by the proportion of each angler type in the angler poplation (0.4 generic; 0.3 consmptive; 0.3 trophy). Parameters vales for the angler-type-specific part-worth-tility (PWU) fnctions (Figre 3) were chosen based on assmptions abot differences among angler types reported in the angler-specialization literatre. Figre 1 illstrates qalitative differences in angler preferences, and Figre 3 illstrates the angler-type-specific tility fnctions based on the parameters listed here. Variable Symbol and defining eqation Rationale for angler-type-specific Parameters vales describing angler types (affected eqation); rationale shape (sorce) Generic Consmptive Trophy Average for general shape (sorce) Importance of fishing to angler lifestyle Basic tility U 0 j (eqation 1b); As specialization increases: basic Lowest Intermediate Highest gained by an Constant fnction: the tility of fishing increases (4, 16); U 0 j = U 0 j = U 0 j = U 0 j = angler of type propensity to fish when all the assmed annal participation (40% (50% (60% (49% 56

58 j from other attribtes are as expected; is generally consistent with stdy probability of probability of probability of probability of choosing to fish see ** for expected vales. findings (7, 10). fishing) fishing) fishing) fishing) Tolerances with regard to managerial constraints PWU of U = r+ r + 2 rj 1j 2 j 3j As specialization increases: Intermediate Lowest Highest minimm-size (eqation 1b), where r is the anglers become less consmptive 1 j = j = j = j = limit for an standardized MSL *; and have a greater acceptance of 2 j = j = j = j = angler of type j Dome-shaped qadratic fnction: anglers may prefer stricter minimm-size reglations (6, 16), bt consmptively 3 j = j = j = j = moderate minimm-size oriented anglers are averse to reglations, bt object to too harvest reglations that limit their low and to too high levels (10, ability to harvest fish (1, 8, 12). 16, 17). PWU of annal U = o (eqation 1b), oj 4 j As specialization increases: cost Lowest Intermediate Highest license cost for where o is the relative license aversion decreases (4, 16). 4 j = j = j = j = an angler of cost**;

59 type j Linear fnction: license costs sally have a negative effect on angler tility (14, 21). Preferences with regard to attribtes of the fishing experience PWU of daily U = c + c 2 cj 5j D 6 j D As specialization increases: focs Intermediate Highest Lowest catch rate for an (eqations 1a and 1b), where shifts from qantity to qality and interest in interest in interest in angler of type j c D is the relative daily catch rate ; Dome-shaped qadratic fnction: greater tility is gained from increasing catch to the challenge of the catch (2, 6, 15). catch Lowest interest in challenge catch Intermediate interest in challenge catch Highest interest in challenge rates (2, 3, 15), bt marginal benefits decrease at high catch 5 j = j = j = j = rates de to the lack of 6 j = j = j = j = challenge (1, 2, 9). 58

60 PWU of U = l + (eqation 1b), sj 7 j 8j As specialization increases: Lowest Intermediate Highest average size of where l is the relative size of importance attached to the size of 7 j = j = j = j = fish captred fish caght ; fish increases (2, 6, 10). 8 j = j = j = j = annally for an Linear fnction: anglers have a angler of type j general preference for catching larger fish (2, 10, 11). PWU of maximm size of U l if l 0 = if < j x x xj 2 9 jlx lx As specialization increases: tility gained from large-sized fish Intermediate 9 j = Lowest 9 j = Highest 9 j = j = fish captred (eqation 1b), where l x is the increases (2, 6, 17), bt the least annally for an relative maximm size (= the specialized, generic anglers gain angler of type j 95 th percentile in the size more tility than consmptive distribtion of fish caght ); anglers in the nlikely event that Piecewise qadratic fnction: they catch a large fish (8). increasing when the relative maximm size is positive and 59

61 decreasing when it is negative; anglers gain greater tility from larger fish (18), and the relative vale of large-sized fish is nonlinear (12). PWU of U = A+ A + 2 aj 10 j 11j 12 j As specialization increases: desire Highest Intermediate Lowest crowding for an (eqation 1b), where A is the for solitde increases (6, 7, 22); 10 j = j = j = j = angler of type j expected daily congestion ; Dome-shaped qadratic fnction: anglers gain tility consmptive anglers recognize that areas with high catch rates will attract other anglers (13). 11 j = j = j = j = j = j = j = j = from the social aspects of fishing, bt avoid congested sites (22). Fishing practices Skill level of an q j (eqation 7b); As specialization increases: skill Lowest Intermediate Highest 60

62 angler of type Measred in terms of level increases (8, 10). q j = q j = q j = q j = j catchability. ha h -1 ha h -1 ha h -1 ha h -1 Size selectivity y j and z j (eqation 7a) As specialization increases: type Small Small Large for an angler of Measred in terms of of fishing gear sed changes (2, y j = 0.21 y j = 0.21 y j = 0.21 y j = 0.21 type j parameters for the size- 6), and gear sed by more cm -1 cm -1 cm -1 cm -1 dependent vlnerability to specialized anglers catches larger z j = 406 z j = 406 z j = 4636 z = 1675 j captre (modified from 20). fish (21). Threshold for c max j (eqation 7e) As specialization increases: Highest Lowest Intermediate practicing Measred in terms of the propensity to harvest fish c max j = 2 c max j = c max j = 0.5 c max j = volntarily desired average nmber of fish decreases (6). catch-and- an angler will harvest daily. release fish for an angler of type j 61

63 Hooking f hj (eqations 7f and 7g) As specialization increases: no mortality for an Measred in terms of the differences in hooking mortality f hj = 0.05 f hj = 0.05 f hj = 0.05 f hj = 0.05 angler of type proportion of fish dying from levels (5) were assmed. j hooking mortality. Non- f nj (eqation 7c) As specialization increases: no compliance Measred in terms of the differences in non-compliance f nj = 0.05 f nj = 0.05 f nj = 0.05 f nj = 0.05 mortality for an proportion of fish nder the were assmed; becase vales angler of type minimm-size limit ( MSL ) reported in the literatre vary j that are harvested illegally. widely (19, 23, 24), a conservative constant vale of 5% was assmed Sorces: (1) Aas and Kaltenborn 1995; (2) Aas et al. 2000; (3) Arlinghas 2006b; (4) Arlinghas and Mehner 2004b; (5) Arlinghas et al. 2008c; (6) Bryan 1977; (7) Connelly et al. 2001; (8) Dorow et al. 2010; (9) Fedler and Ditton 1994; (10) Fisher 1997; (11) Gillis and Ditton 2002; (12) Jacobson 1996; (13) Martinson and Shelby 1992; (14) Massey et al. 2006; (15) Oh and Ditton 2006; (16) Oh et 62

64 al. 2005a; (17) Oh et al. 2005b; (18) Palrd and Laitila 2004; (19) Pierce and Tomcko 1998; (20) Post et al. 2003; (21) Rapp et al. 2008; (22) Schhmann and Schwabe 2004; (23) Sllivan 2002; (24) Walker et al r = MSL L is the relative minimm-size limit, standardized to range between 0 and 1, where L max is the maximm size that a * / max fish can attain at the maximm age allowed in the absence of density dependence (eqations 4a-d). o= ( O O ) is the annal fishing-license cost relative to a baseline expected vale, where O o and ** o e expected vales, respectively. O e are the observed and Attribtes related to the fish poplation represent the proportional difference scaled relative to a baseline expected vale as follows: cd = CDo / CDe 1, where C Do and C De, respectively, are the observed and expected average daily catch rates; l = Lo / Le 1, where L o and L e, respectively, are the observed and expected average sizes of caght fish in a year; l x = L xo / L xe 1, where L xo and L xe, respectively, are the observed and expected the maximm sizes of caght fish in a year (with the latter defined as the 95 th percentile of the size distribtion of caght fish). Expected vales are based on the literatre and on npblished data from pike fisheries. We assmed an expected daily catch rate of 0.5 fish (Kempinger and Carline 1978; Goeman et al. 1993; Arlinghas et al. 2008c) and that anglers fished 4 h in an angling day, an expected average size of 51 cm (Kempinger and Carline 1978; Pierce et al (harvested fish); Arlinghas et al. 2008c), and an expected average maximm size of 69 cm (Dorow and Arlinghas, npblished data). 63

65 1179 A= ( DjA j) / (365 S ) is the expected average nmber of anglers fishing in a day (see eqations 2c-d). j L F

66 Table 4 Predicted optimal reglation and their implications. Optimal inpt and otpt reglations maximized social welfare for varios angler types and for different assmptions abot angler behavior and social-welfare measres. Implications are shown in terms of reslting angling efforts and biological impacts (with the latter being measred by the spawning-potential ratio SPR ). Three social-welfare measres were examined for the mixed angler poplation: total tility (TU), an eqitable tilitarian tility (EU) and a Rawlsian tility (RU) ( Table 1, eqations 8 a-c). For the non-mixed angler poplations, reslts for the EU and R were identical to those for TU and are therefore not repeated. Scenario Angler poplation Generic Consmptive Trophy Average Mixed Optimal minimm-size limit (cm) Static TU Catch-based TU Mlti-attribte TU (EU; RU) (69; 63) Optimal angler-license nmber Static TU Catch-based TU Mlti-attribte TU (EU; RU) (48; 48) Annal realized angling effort nder optimal reglations (h ha -1 ) Static TU Catch-based TU Mlti-attribte TU

67 (EU; RU) (57; 57) Composition of anglers fishing in the mixed angler poplation nder optimal reglations Static TU n.a n.a Catch-based TU n.a n.a Mlti-attribte TU n.a n.a (EU; RU) (0.38; 0.37) (0.27; 0.29) (0.35; 0.34) Spawning-potential ratio nder optimal reglations Static TU Catch-based TU Mlti-attribte TU (EU; RU) (0.57; 0.48)

68 Figre captions Figre 1 Simplified flow diagram illstrating interactions among the three model components of or bioeconomic modelling approach: the biological component, the socioeconomic component, and the management component. The model inclded three angler-behavior scenarios: (a) static angler behavior, where anglers fish at the maximal rate; (b) catch-based dynamic angler behavior, where anglers responded to the fishery based on catch rates; (c) mlti-attribte dynamic angler behavior, where anglers responded to the fishery based on a mlti-attribte tility fnction. Black, solid arrows depict inflences that apply across all scenarios, while gray arrows apply to the catch-based scenario only and black dashed arrows apply to either the static or mlti-attribte scenarios as is also indicated by labels along the arrows. Factors in rond-cornered boxes dynamically change throghot model rns, while parameters for factors in sqare-cornered boxes were held constant Figre 2 Qalitative differences in angler preferences for fishery attribtes among the three different prototypical angler types (generic, consmptive, and trophy anglers). Gray circles indicate the relative preference levels or tolerance levels (low, intermediate, or high) of angler types for a particlar fishery attribte Figre 3 Part-worth-tility fnctions describing the preferences of generic, consmptive, trophy and average anglers for varios attribtes of the fishery Figre 4 Total tility (TU) over a range of inpt (license nmber) and otpt (minimm-size limit) reglations. Colmns illstrate reslts for three angler- behavior scenarios (left colmn: static angler behavior, where anglers fished at the 67

69 maximal rate; middle colmn: catch-based dynamic angler behavior, where anglers responded to the fishery based on catch rates; right colmn: mlti-attribte dynamic angler behavior, where anglers responded to the fishery based on a mlti-attribte tility fnction). Rows illstrate reslts for five different angler poplations (first row: generic anglers; second row: consmptive anglers; third row: trophy anglers; forth row: average anglers; and fifth row: mixed angler poplation composed of 40% generic, 30% consmptive, and 30% trophy anglers). Ble diamonds indicate the optimm reglations at which total tility was maximized Figre 5 Spawning-potential ratio ( SPR ) of fished poplations over a range of inpt (license nmber) and otpt (minimm-size limit) reglations. SPR vales below indicate a potential for recritment overfishing. Colmns show reslts for three angler-behavior scenarios (left colmn: static angler behavior, where anglers fished at the maximal rate; middle colmn: catch-based dynamic behavior, where anglers responded to the fishery based on catch rates; right colmn: mlti-attribte dynamic behavior, where anglers responded to the fishery based on a mlti-attribte tility fnction). Rows show reslts for five different angler poplations (first row: generic anglers; second row: consmptive anglers; third row: trophy anglers; forth row: average anglers; fifth row: mixed angler poplation composed of 40% generic, 30% consmptive, and 30% trophy type anglers). Ble diamonds indicate the optimm reglations at which total tility was maximized Figre 6 Proportion of the total realized angling effort contribted by each angler type in a mixed angler poplation over a range of inpt (license nmber) and otpt (minimm-size limit) reglations. The mixed angler poplation was composed of 68

70 % generic, 30% consmptive, and 30% trophy type anglers. Anglers responded to the fishery based on a mlti-attribte tility fnction; see (o) panels in Figres 4 and 5. Ble diamonds indicate the optimm reglations at which total tility was maximized Figre 7 Social-welfare measres in a mixed angler poplation with mlti-attribte dynamic angler behavior over a range of inpt (license nmber) and otpt (minimm-size limit) reglations. The mixed angler poplation was composed of 40% generic, 30% consmptive, and 30% trophy anglers. Reslts are shown for three social-welfare measres (total tility, TU;, egalitarian tilitarian tility, EU; Rawlsian tility, RU; see Table 1, eqations 8a-c). Ble diamonds indicate the optimm reglations at which the social-welfare measres were maximized. 69

71 Socioeconomic component (a) Static (b) Catch-based (c) Mlti-attribte Realized fishing effort Maximm fishing effort possible Probability of fishing (a) & (c) (b) Management component (b) (a) & (c) Welfare measre (e.g., total tility) Max Optimal reglations: MSL & license no. Utility from fishing Catch-based tility Mlti-attribte tility Fishery attribtes Catch Average size of fish captred Maximm size of fish captred Propensity to fish MSL License cost Crowding Fish vlnerability & angler skill Volntary catch & release Figre 1 Reprodction: plsed at the beginning of the year Biological component Growth: biphasic, density-dependent growth that is continos throghot the year Srvival: Natral: density-dependent age-0 srvival at beginning of year & constant continos age-1+ mortality Fishing: continos mortality from harvest, non-compliance, and hooking mortality 70

72 Tolerance for attribte Preference for attribte Crowding Fishing Catch rate Challenge High Intermediate Low Generic Consmptive Trophy MSL Mean size Cost Max. size Tolerance for attribte Preference for attribte Figre 2 71

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