Are marine reserves and harvest control rules substitutes or complements for rebuilding fisheries?

Resource and Energy Economics 40 (2015) 1–18

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Are marine reserves and harvest control rules substitutes or complements for rebuilding fisheries? Satoshi Yamazaki a,∗, Sarah Jennings a, R. Quentin Grafton b, Tom Kompas b a Tasmanian School of Business and Economics, University of Tasmania, Private Bag 84, Hobart, TAS 7001, Australia b Crawford School of Public Policy, Lennox Crossing, The Australian National University, Canberra, ACT 2601, Australia

a r t i c l e

i n f o

Article history: Received 17 August 2013 Received in revised form 7 January 2015 Accepted 9 January 2015 Available online 19 January 2015 Keywords: Fisheries management Harvest control rules Marine reserves Stock recovery plans

a b s t r a c t Harvest control rules and no-take marine reserves are two management approaches increasingly advocated as effective means of rebuilding depleted fish stocks and averting the collapse of fisheries. We incorporate the two approaches into a bioeconomic model and evaluate how they act as substitutes and/or complements when used together in fisheries stock recovery plans. Simulations of the model with estimated parameters from an actual fishery show that the cost of adopting a harvest strategy of slow stock rebuilding can be offset or substituted by a no-take reserve. For each of the harvest strategies explored, we find there is a range of reserve sizes that can act as a complement in a stock recovery plan such that a no-take reserve improves both the profitability of fishers and average annual harvest during stock rebuilding. We demonstrate that a stock recovery plan that incorporates both harvest control rules and no-take reserves can simultaneously contribute to conservation, economic and socio-economic objectives of fisheries management. © 2015 Elsevier B.V. All rights reserved.

∗ Corresponding author. Tel.: +61 3 62262820. E-mail addresses: [email protected] (S. Yamazaki), [email protected] (S. Jennings), [email protected] (R. Quentin Grafton), [email protected] (T. Kompas). http://dx.doi.org/10.1016/j.reseneeco.2015.01.001 0928-7655/© 2015 Elsevier B.V. All rights reserved.

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1. Introduction The importance of rebuilding already depleted fish stocks and the need to prevent further collapse of fisheries worldwide is uncontentious (Worm et al., 2009; OECD, 2010). Recent studies demonstrate the biological and economic benefits of stock rebuilding and averting fisheries collapse (Arnason et al., 2009; Sumaila et al., 2012; Costello et al., 2012). Despite the potential payoffs, according to the Food and Agricultural Organization of the United Nations, about 30% of assessed fish stocks are overexploited and need rebuilding (FAO, 2012) and overfishing remains a threat to marine species and ecosystems (Halpern et al., 2008). Stock recovery plans have been implemented in many fisheries around the world to reduce fishing mortality, but with mixed success (Caddy and Agnew, 2004; Rosenberg et al., 2006; Murawski, 2010). Factors found to be associated with the successful recovery plans include the deployment of measures that effectively control fishing mortality and, in addition, a legal and stakeholder mandate for fisheries managers to give priority to long-term biological, ecosystem and economic benefits over shorter term and socio-economic outcomes (Murawski, 2010). There are a number of management approaches available to reduce fishing mortality rates, including rules to directly control harvest levels (Gooday et al., 2010; Froese et al., 2011; Costello et al., 2012) and the establishment of no-take marine reserves in which harvesting is prohibited (Roberts et al., 2005; Gaines et al., 2010). Harvest control rules that are underpinned by monitoring and assessment of the status of the target stock provide a scientific basis for setting catch limits (Smith et al., 2008; Punt, 2010). Harvest control rules also provide a necessary condition for the implementation of rights-based catch shares that can enhance fisheries sustainability (Grafton et al., 2006a) and decrease the chance of fisheries collapse (Costello et al., 2008). Likewise, the establishment of no-take marine reserves has been promoted in many countries as a way to control fishing mortality, thereby restoring depleted fish stocks as well as enhancing the sustainability of fisheries (Roberts et al., 2005). There is evidence that the implementation of no-take reserves can increase fish biomass, individual fish size, and species richness within reserve boundaries (Lester et al., 2009). No-take marine reserves are frequently presented as an alternative management approach to harvest control rules in the recovery of declining fisheries. In part this is because marine reserves, relative to harvest control rules, have been shown to help to mitigate irreducible management error and environmental uncertainty (Lauck et al., 1998; Mangel, 2000) that, in turn, decreases the chance of fishery collapse (Grafton et al., 2009). Nevertheless, the enforcement of a no-take reserve alone is insufficient to achieve conservation goals (Allison et al., 1998). This is because the efficacy of reserves as a fisheries management tool critically depends, among other things, on management of the fishery outside the reserve, including harvest control rules (Hilborn et al., 2004, 2006; Armstrong and Skonhoft, 2006; Sumaila and Armstrong, 2006; White and Costello, 2010; Costello and Kaffine, 2010; Rassweiler et al., 2012; Yamazaki et al., 2012). In this paper we explore how harvest control rules and no-take reserves perform when used jointly in fisheries stock recovery plans. Previous studies have provided the conditions under which the two management approaches separately contribute to successful rebuilding outcomes (Larkin et al., 2006; Gooday et al., 2010; Costello et al., 2012). Researchers have also examined the effects of reserve establishment when the fishery is managed in conjunction with an economically optimal harvest strategy (Neubert, 2003; Schnier, 2005; Grafton et al., 2006b, 2009; Sanchirico et al., 2006, 2010; Little et al., 2010b; Yamazaki et al., 2010). To date, however, there has been no study that has quantitatively modeled and evaluated how the two approaches are substitutes and/or complements in rebuilding fisheries. To this end, we assess the performance of alternative stock recovery plans to quantitatively explore: one, whether harvest control rules and no-take marine reserves are substitutes in hastening the speed of recovery of a fishery; and two, whether no-take reserves and harvest control rules are complementary in terms of their effects on the speed of stock rebuilding, the net present value of the fishery and average annual harvest during the rebuilding phase; and three, how the two management approaches interact when used jointly to affect the tradeoffs between potentially conflicting fisheries objectives. The rest of the paper is structured as follows. Section 2 develops a bioeconomic model of a fishery that allows for the implementation by a management authority of a stock recovery plan aimed at

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rebuilding the population biomass to a target level that involves combining no-take reserves of different sizes with alternative stock rebuilding harvest strategies. Given that both reserve establishment and the optimal rebuilding path have been shown to be sensitive to different types of uncertainty (Wilen and Brown, 1986; Lauck et al., 1998; Mangel, 2000; Grafton et al., 2006b; Kvamsdal, 2011), the bioeconomic model incorporates two forms of environmental uncertainty. Sections 3–5 report simulation results for a parameterized version of our bioeconomic model. The outcomes of alternative stock recovery plans are reported against three fisheries performance indicators, corresponding to the conservation, economic and socio-economic objectives of fisheries management. Section 6 provides both a discussion of the results and concluding remarks. 2. Methods Following earlier studies of marine reserves (Hannesson, 1998; Conrad, 1999; Sanchirico and Wilen, 2001; Grafton et al., 2006b) we construct a bioeconomic model that integrates a population model of biomass dynamics and an economic model of the fishery. The total population (x) is divided into the harvest population (xH ) and the reserve population (xR ) such that xt = xtH + xtR .1 Time is indexed by t = 0, 1, 2, . . .. 2.1. Biomass dynamics model The biomass dynamics of the two sub-populations (xH and xR ) are modeled as:



g

H xt+1 = xtH − tH xtH + zt rxtH

1−

 g

R = xtR − tR xtR + zt rxtR xt+1

1−

xtH [1 − s]K

xtR sK





+ m(1 − s)K



 − m(1 − s)K

xtH xtR − sK [1 − s]K

xtH xtR − sK [1 − s]K



− ht

(1)

 (2)

where ht in (1) is the harvest at time t and harvest of the reserve population is not permitted. The size of the no-take reserve is defined in the population-based bioeconomic model as the proportion of the population carrying capacity (K) that is not exposed to fishing which is denoted by the parameter s ∈ [0, 1] (Hannesson, 1998; Conrad, 1999; Grafton et al., 2006b).2 The third term on the right hand side of each of the equations is the population-specific growth function where r is the intrinsic growth rate. The fourth term of Eqs. (1) and (2) represents the transfer function that links the harvest and the reserve populations, in which the parameter m ≥ 0 is the transfer coefficient that determines the strength of connectivity between the two populations. There is increasing evidence that no-take reserves generate a spillover effect in terms of one, adult and larval export from the reserve to adjacent fished areas and, two, higher catch and catch rate on the reserve boundaries (McClanahan and Mangi, ˜ et al., 2010; Harrison et al., 2012). The transfer func2000; Russ et al., 2004; Stobart et al., 2009; Goni tion is specified in the same or a similar way elsewhere (Hannesson, 1998; Conrad, 1999; Sanchirico and Wilen, 2001; Schnier, 2005; Grafton et al., 2006b; White and Costello, 2011). Further, this specification reflects empirical observations that fish dispersion is density-dependent due to local negative

1 A discrete two-population model permits us to consider the harvest and reserve populations explicitly, but note that the model does not incorporate some features of marine capture fisheries, such as the spatial dynamics of fishers’ behavior, heterogeneity within the fishing area, and possible ‘edge’ effects whereby fishing effort may concentrate on the reserve boundary (Holland, 2000; Sanchirico and Wilen, 2001; Smith and Wilen, 2003; Kahui and Alexander, 2008; Hicks and Schnier, 2010; Rassweiler et al., 2012). 2 We confine our analysis to a permanent prohibition of fishing within the reserve. Earlier studies examining the effects of permanent reserves are Polacheck (1990), Holland and Brazee (1996), Hannesson (1998), Conrad (1999) and Sanchirico and Wilen (2001). This is in contrast to some other studies that have examined the effects of alternative forms of no-take reserves, such as a temporal area closure or optimal closure strategy (Costello and Polasky, 2008; Little et al., 2010a; Yamazaki et al., 2010).

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interactions of competing foods, territories and breeding partners (e.g., Rosenberg et al., 1997; Kramer and Chapman, 1999; Abesamis and Russ, 2005).3 The biomass dynamics specified in Eqs. (1) and (2) incorporates two forms of environmental uncertainty. The first form is the variability in the population growth that occurs as a result of temporal variation in the environment (Caddy and Gulland, 1983; Hofmann and Powell, 1998). g g This form of uncertainty is captured in the model by the random variable zt where E[zt ] = 1, and   g g g g g g g zt ∈ Z g = z1 , z2 , . . ., zN with z1 < z2 < · · · < zN . We assume that the occurrence of environmental



g

g

 

g

g

variability follows a Markov chain, such that Pr zt+1 = zj  zt = zi



= pji ≥ 0 and

N

p j=1 ji

= 1 for all i.

The second form of environmental uncertainty is a random negative population shock, denoted as ti , i = H, R, in Eqs. (1) and (2). Both the harvest and reserve populations are subject to random events that negatively impact on the level of biomass through, for example, a natural disaster, the poor recruitment of juveniles in a particular year or habitat degradation due to human activity (Caddy and Gulland, 1983; Hofmann and Powell, 1998; Jennings et al., 2001). The random variable, ti , takes the   form ti = ωti i where i ∈ [0, 1] is the size of the negative shocks and ωti ∈ ˝ = 0, 1 is an indicator variable such that a negative shock is realized for the population i at time t if ωti = 1 and there is no shock otherwise.4 The random negative shocks follow  chain

ai Markov  and the probability of realizing a shock on the population i at time t is given by Pr ωt+1 = 1 ωti = ˛i ≥ 0 where the parameter ˛i represents the arrival rate of shocks. 2.2. Net present value of fishing We specify the net profit function of the fishery as:





 ht , xtH , s = P (ht ) ht − C ht , xtH , s

(3)

where P(.) is the inverse demand function and C(.) is the harvesting cost function. The inverse demand function is specified as P(.) = ph−1/ε where ε is the price elasticity of demand and p is a parameter

 (Clark, 1990). The harvesting cost function is specified as C(.) = c(1 − s)/xtH ht where c is a parameter (Grafton et al., 2006b). This specification accounts for the sensitivity of the harvesting cost to the density of a fish population. More precisely, the marginal cost of harvesting

decreases as the density

of the harvested population increases ceteris paribus, i.e., ∂2 C(.)/ ∂xtH ∂ht < 0 and ∂2 C(.)/ ∂s∂ht < 0 (Grafton et al., 2007; White et al., 2008).5 This characteristic of the harvesting cost is known as the stock effect and previous research empirically finds that the stock effect exists for many fish stocks; yet the strength of such an effect varies across fisheries (Bjørndal, 1987; Grafton et al., 2007; Hannesson, 2007; Kompas et al., 2010a,b). Further, there is empirical evidence that the catch per unit of effort decreases with the establishment of no-take reserves, suggesting that the reserve establishment decreases the marginal harvesting cost (Russ et al., 2004; Stobart et al., 2009). Given the net profit function in (3), the net present value (NPV) of the fishery is specified as: NPV =

∞ 



ˇt  ht , xtH , s

(4)

t=0

where ˇ = 1/(1 + ), and  ∈ [0, 1] is the discount rate.

3 The density-dependent and -independent characteristics of the movement of adults and juveniles are discussed by Grüss et al. (2011). 4 For conciseness, we assume that the size of the negative shocks is fixed while the occurrence of each negative shock is probabilistic. The effects of different assumptions about negative population shocks on the biological and economic outcomes of no-take reserves are examined elsewhere (e.g., Grafton et al., 2006b; Kvamsdal, 2011; Yamazaki et al., 2012). 5 It is important to note that our specification of the cost function does not imply that the introduction or expansion of the no-take reserve always decreases the marginal cost of harvesting. In fact, the marginal cost may increase with the establishment of a reserve if the reserve decreases the size of the harvest population and harvesting becomes more expensive as the density of the harvest population declines.

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2.3. Harvest control rule and stock rebuilding harvest strategies In order to assess the relationship between the use of no-take reserves and different harvest strategies in restoring fisheries, we specify a general harvest control rule as:



ht =

h∗t , if xt < xTARGET

(5)

h∗t , if xt ≥ xTARGET

where ≥ 0 is a parameter and xTARGET is the target level of total population biomass (i.e., xH and xR ) which is the same in all stock recovery plans.6 The harvest control rule in (5) implies that the annual catch limit in each year is based on the observed level of total population biomass, xH and xR . For any observed level of total biomass greater than xTARGET the annual catch limit for all harvest strategies is set at h∗t , that is the level that maximizes the expected NPV of the fishery for a given reserve size, s, and, in our model, ensures transition to the stable target, xTARGET . However, for any observed level of population biomass that is below the target level, the annual catch limit depends on the parameter . The optimal harvest strategy involves setting = 1 and implies that the annual catch limit over the rebuilding period is also set at the level that maximizes the expected NPV of the fishery for a given reserve size. Alternative harvest strategies are specified relative to the optimal harvest strategy. If < 1, the annual catch limit is set below the optimal level whenever the biomass is below the target level. Consequently, the duration of the stock rebuilding period is shorter than when the fishery is managed under the optimal harvest strategy ( = 1). By contrast, if > 1, the depleted fish stock is rebuilt to its target level over a longer time period than when the optimal harvest strategy is used because the annual catch limit is set above the optimal level whenever the biomass is below the target level. The three cases of the harvest control rule ( = 1, < 1, > 1), therefore, represent optimal, fast and slow stock rebuilding harvest strategies. The slow stock rebuilding harvest strategy is of particular interest because fisheries managers may not be capable of reducing harvest to the level associated with the optimal harvest strategy due to other policy considerations, such as maintaining short term harvest and employment (Dichmont et al., 2010). 2.4. Optimal harvest strategy and biomass target Given that the future condition of the fishery depends on the realization of the growth uncertainty g (zt ) and negative population shocks (ωtH and ωtR ), the optimal harvest strategy maximizes the expected, instead of the realized, NPV from fishing. Letting E0 be the conditional expectation on the information available at time t = 0, the optimal harvest strategy can be derived by solving the maximization problem given as: max E0 {ht }∞ t=0

∞ 



ˇt  ht , xtH , s

(6)

t=0 g

subject to the biomass dynamics (1) and (2), reserve size, and the initial conditions x0H , x0R , z0 , ω0H , and ω0R .7 This sequential problem can be written as the Bellman equation given as:



v xH , xR , z g , ωH , ωR =

max

h∈ (xH ,xR ,z g ,ωH ,ωR ,s)



 h, xH

+ ˇE











v xH , xR , z g , ωH , ωR



 g H R  z ,ω ,ω

(7)

6 The harvest control rule given in (5) is classified as a feedback control rule, which sets the catch limit for a specified time period based on information on the current stock size (Clark, 1990). The use of different types of feedback control rules in natural resource management in terrestrial and marine environments are discussed in, for example, Homans and Wilen (1997), Sandal and Steinshamn (2001), Aanes et al. (2002), and Arnason et al. (2004). 7 We note that the maximization problem is not subject to the harvest control rule given in (5). This means that the optimal harvest strategy h∗t is independent of which enables us to define the fast and slow stock rebuilding harvest strategies by setting < 1 and >1, respectively.

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where v(.) is the value function, E . z g , ωH , ωR is the expectation conditional on the current values of the random variables (z g , ωH , and ωR ), and (.) is the set of all feasible harvest levels, which depends on the size of the harvest and reserve populations, and hence the reserve size, as well as the realizations of z g , ωH and ωR . The dynamic programming problem in (7) is solved numerically using Matlab. We first discretize the state space of the harvest and reserve populations, such that xtH ∈ X H and xtR ∈ X R with      X H = xtH 0 ≤ xtH ≤ (1 − s)K and X R = xtR 0 ≤ xtR ≤ sK . We then use the value iteration method to calculate the optimal harvest strategy sizes of each for given

population, realization of each random g variable, and reserve size, i.e., h∗t = xtH , xtR , zt , ωtH , ωtR , s . The optimal harvest is bounded within ∗ H the maximum size of the harvest population,  such that ht ⊂ X . The iteration of the value function is terminated when the stopping criterion, vi − vi+1  < 1−10 where i = 1, 2, . . ., is satisfied. ∞ We set the biomass target (xTARGET ) at the population biomass level associated with the dynamic Maximum Economic Yield (xDMEY ) where there is no reserve established, that is the steady-state level of the biomass that maximizes the expected NPV of the returns to fishing when s = 0 (Grafton et al., 2010, 2012).8 While other targets, such as the biomass level associated with the Maximum Sustainable Yield (xMSY ), are possible, the xDMEY target is consistent with the way in which we determine the optimal harvest with s = 0 in Eq. (6). The xDMEY target is calculated by solving the maximization problem in (6) for the case where no reserve is established (s = 0) and is used throughout the paper in assessing all stock recovery plans. Having a common biomass target means that our comparison of alternative stock recovery plans is not confounded by changes in the biomass target for different reserve sizes (s) and harvest strategies ( ). To calculate xDMEY , given the random temporal variation in total biomass, we simulate 10,000 Monte Carlo samples of total biomass when the fishery is managed in conjunction with the optimal harvest strategy ( = 1) and with no reserve (s = 0) for 500 periods. We then use the last 100 periods of the simulated series to calculate the mean value of total biomass as the dynamic xDMEY target level, that is:

 g

1 H R xt,m zt,m , ωt,m , ωt,m (T − tˆ)M M

xDMEY =

T

(8)

m=1 t=tˆ

where M = 10,000, T = 500 and tˆ = 401. 3. Substitutability and complementarity of no-take reserves and harvest control rules in rebuilding fisheries The bioeconomic model developed in Section 2 is simulated with the estimated parameter values reported in Grafton et al. (2006b) for the Pacific halibut fishery. The benchmark parameter values used in the simulations are summarized in Table 1. We emphasize that our purpose is not to provide an empirical assessment of a specific fishery, but rather to develop insights about how the harvest strategy and no-take reserves perform when used together in fisheries stock recovery plans.9 The effects of changes in biological and environmental conditions using scenario analysis are given in Section 5. We report against three fisheries performance indicators corresponding broadly to the conservation, economic and socio-economic objectives of fisheries management. These are: one, the number of years taken to first rebuild the total population to its biomass target level (i.e., stock rebuilding

8 It is important to note that the biomass level that maximizes the expected NPV of the returns to fishing varies for different sizes of the no-take reserve. We, however, use the same target, which corresponds to the no reserve case, for all recovery plans so that our results are not confounded by the shift in the target. How the population biomass target is affected by different reserve sizes and alternative stock rebuilding harvest strategies is beyond the scope of this paper. The effects of reserve size on the biomass target are examined by Yamazaki et al. (2012). 9 Advantages and disadvantages of generic modeling against case study based empirical analysis have been long discussed. We maintain that both approaches can provide valuable insights into the effectiveness of natural resource management policy in complex dynamic systems. For example see Haddon (2011) and van den Bergh et al. (2010).

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Table 1 Benchmark parameter values. Parameter

Description

Value

 p ε c r K m  ˛

Time discount rate (per year) Price parameter (US dollars) Price elasticity of demand (|%h/%P|) Cost parameter (US dollars) Intrinsic growth rate (per year) Carrying capacity (million pounds) Transfer coefficient Standard deviation of environmental uncertainty Size of negative shocks (proportional to the stock size) Arrival rate of negative shocks (per year)

0.0500 0.0700 1.2346 0.1710 0.2985 0.9631 0.1000 0.0297 0.1300 0.0400

period),10 two, the NPV of the fishery and, three, the average annual harvest in the first 10 years of the stock rebuilding phase.11 We simulate the model for 500 periods to obtain 10,000 Monte Carlo samples of the performance indicators for 25 stock recovery plans defined as combinations of five no-take reserve sizes including the no-reserve case (s ∈ {0, 0.1, 0.2,  0.3, 0.5}) and fivestock rebuilding harvest strategies including the optimal harvest strategy ( ∈ 0.6, 0.8, 1, 1.2, 1.4 ).12 We standardize each outcome relative to the baseline stock recovery plan which combines the optimal harvest strategy with no-reserve ( = 1 and s = 0), thus allowing us to compare the relative effects of alternative stock recovery plans that incorporate reserves of different sizes with alternative stock rebuilding harvest strategies. Given our focus on stock rebuilding in depleted fisheries we set the initial biomass at a level less than the target biomass level (x0 < xTARGET = xDMEY ) and use the biomass level associated with the bionomic equilibrium (Gordon, 1954) as the initial condition in the fishery. Using the parameter values in Table 1, the harvest and biomass levels associated with the bionomic equilibrium are calculated at 0.05 and 0.2160 million pounds, while the dynamic xDMEY target level in Eq. (8) is at 0.8183 million pounds. The NPV of the fishery is positive for all stock recovery plans examined in this paper and therefore greater than the NPV of the fishery at the bionomic equilibrium where all economic profits are dissipated. 3.1. Duration of stock rebuilding period Fig. 1 presents the relative change in the number of years required to first restore the total population biomass to its xDMEY target level for the 25 stock recovery plans. As expected, for recovery plans involving a given reserve size, the stock rebuilding period is reduced the more restrictive is the harvest control rule. For instance, in the case where there is no reserve established (s = 0) and the harvest is restricted to 60% of the optimal level ( = 0.6), the number of years taken to rebuild the fish stock is on average 22.3% shorter than in the baseline recovery plan. By contrast, setting the harvest above the optimal level lengthens the stock rebuilding period and may even prevent the depleted stock rebuilding to the target level. For instance, when the recovery plan adopted sets the level of harvest 40% above the optimal level and does not establish a reserve

10 Alternatively, we may calculate the number of years taken to first rebuild the total population to its biomass target level and the stock remains at or above the target level for the next 10 years in 95% of cases. This is a stricter criterion to determine the stock rebuilding period than the one we use in this paper as it excludes the case where the stock reaches the target level by accident due to variability in biomass. We note that using this alternative rebuilding criterion does not qualitatively change the results. 11 Average catch or harvest is a broad performance indicator of the socio-economic status of the fishery because the volume of fish landings is positively correlated with employment and other aspects of livelihood (Hilborn, 2007). An extensive list of biological, economic and socio-economic indicators for assessing the effects of coral reef marine protected areas is discussed in Pelletier et al. (2005). For example, another indicator representing the economic performance of alternative rebuilding strategies is the cost of fishing during the rebuilding period. 12 We note that not all possible stock recovery plans will be available to managers, as there may be constraints on the range of harvest levels and reserve sizes that are socially and politically acceptable.

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Fig. 1. Relative effect of reserve size and stock rebuilding harvest strategies on the duration of the rebuilding period. The baseline case is s = 0 and = 1. The mean ±95% confidence interval. The colored lines are quadratic fit for each . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

( = 1.4 and s = 0), there is a 88% chance that the biomass cannot be rebuilt to its xDMEY target level over the simulation period.13 Furthermore, keeping the harvest level above the optimal level results in increased variability in the stock rebuilding period. This is because the higher the harvest the greater the variation in biomass. Nevertheless, increasing the size of the no-take reserve partly offsets the increase in the length of the stock rebuilding period and, therefore, reduces the possibility of not being able to rebuild the depleted fishery to its target biomass and decreases variability in the stock rebuilding period. In particular, placing 10% of the carrying capacity in a no-take reserve in conjunction with the slow rebuilding harvest strategy ( = 1.4 and s = 0.1) reduces the possibility that the stock cannot be successfully rebuilt to 0% while the number of years taken to rebuild the fish stock is on average 157% longer than the baseline case. Further, our results show that increasing the size of the reserve to 50% of the carrying capacity continues to partially offset the longer rebuilding duration associated with the slow rebuilding harvest strategy. The average number of years required to rebuild the depleted fish stock becomes only 16.5% longer than for the baseline recovery plan for the stock recovery plan combining = 1.4 and s = 0.5. An increase in the size of the no-take reserve also reduces the duration of the rebuilding period in recovery plans that adopt the harvest control rule associated with the optimal harvest strategy ( = 1). For instance, in our model increasing the reserve size from 0% to 30% in such a plan shortens the stock rebuilding period, on average, by 7.1%. By contrast, if the harvest is already restricted below its optimal level for a fast recovery of the depleted stock, to say 60% ( = 0.6), the benefit of reserve establishment, in terms of how quickly the depleted stock is rebuilt to its target level, is negligible (<1%).

13 Given the fishery is not rebuilt to the target level within the simulation period for a large proportion of the Monte Carlo samples, the mean and a 95% confidence interval are not shown in Fig. 1.

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Fig. 2. Relative effect of reserve size and stock rebuilding harvest strategies on the NPV of fishing and the average harvest for the first 10-year of the rebuilding period. The baseline case is s = 0 and = 1. The mean ±95% confidence interval. The colored lines are quadratic fit for each . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Our findings suggest that no-take reserves can reduce the time taken to rebuild the depleted fish stock to the target biomass level when combined with either the optimal or a slow rebuilding harvest strategy. Relative to the baseline recovery plan and for the range of reserve sizes explored, the establishment of a no-take reserve comprising up to half of the population carrying capacity acts as a temporal substitute for a harvest strategy that slows the stock recovery process. 3.2. Net present value of fishing and 10-year average annual harvest Fig. 2 shows the relative effects of the different stock recovery plans on the economic and socioeconomic performance indicators for the fishery, namely the NPV of fishing (Fig. 2a) and the average annual harvest in the first 10 years of the stock rebuilding phase (Fig. 2b).14 Regardless of the harvest strategy adopted in the recovery plan, the establishment of a no-take reserve of 10% of the population carrying capacity improves both the NPV of fishing and the 10-year average harvest relative to the no reserve case. Further, when combined with the optimal harvest strategy, the 10% reserve results in a double-payoff in terms of both economic and socio-economic performance. More particularly, when 10% of the total population is placed in the reserve and the optimal harvest strategy is adopted, there is a more than 95% and 75% chance that the NPV of fishing and the average harvest in the first 10 years of the rebuilding phase increase relative to the baseline recovery plan ( = 1 and s = 0).15 We observe the complementarity between the reserve establishment and optimal harvest strategy due to synergistic benefits of the two approaches, which have been documented separately in the literature. The first of such benefits is that, while an increase in the reserve size limits the fishable area, establishment of the no-take reserve provides the fishery with an increased ability to hedge stochastic variations in fisheries (Lauck et al., 1996; Mangel, 2000; Sumaila, 1998; Grafton et al., 2006b, 2009). In our simulation, this effect is reflected in our observation that the speed of stock recovery

14

We calculate the NPV of fishing by simulating the model over 500 periods. This also means that we can reject the null hypothesis that the NPV of fishing for the no-reserve and 10% reserve case is the same at the 5% level of statistical significance, whereas we cannot reject the null hypothesis that the average harvest for the no-reserve and 10% reserve case is the same at the 5% level. In other words, hypothesis testing at the 5% significance level can be conducted by inspecting whether the confidence interval overlaps the zero line or not. However, given we obtain the distribution of performance indicators through Monte Carlo simulation, hereafter, we discuss the results based on the simulated distribution instead of the results of hypothesis testing. 15

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Fig. 3. Mean difference over time in the (1) total biomass, (b) net profit of fishing, and (c) harvest between the case of a positive reserve size (s = 0.1, 0.2, 0.3, or 0.5) with the optimal harvest ( = 1) and the baseline case (s = 0 and = 1). Based on 10,000 Monte Carlo samples.

to the target level is faster when the fishery is managed with the reserve than without the reserve (Fig. 1). This observation is consistent with the concept of resilience defined by Pimm (1984), such that the reserve reduces the time taken for the variable of interest (total biomass) to return to its equilibrium (target) following a perturbation. Secondly, the harvest control rule in (5) is developed based on the optimal harvest strategy that adjusts the level of the annual allowable harvest during the rebuilding period in response to changes in reserve size so as to rebalance the marginal benefit and cost of additional harvest over time (Sanchirico et al., 2006; Yamazaki et al., 2012). Conversely, if the allowable annual harvest were not modified according to the change in the reserve size, the reserve establishment may even decrease the overall stock abundance and harvest (Hilborn et al., 2006). In effect, the establishment of the reserve complements the optimal harvest strategy, increasing both the NPV of fishing and the average harvest during stock rebuilding. This complementarity between the two rebuilding approaches is evident in our simulations for a reserve of 10% of the population carrying capacity in recovery plans that incorporate either slow or fast rebuilding harvest strategies. In the slow recovery case ( = 1.4) the NPV of fishing increases by 0.3% and the 10-year average harvest increases on average by 3.8%, relative to the no-reserve alternative. In the fast case ( = 0.6) the relative gains in the two performance indicators are higher, on average, by 0.3% and 5.4%. Additional complementarity between the reserve establishment and alternative stock rebuilding harvest strategies, in terms of the ability of the no-take reserves to increase both the NPV of fishing and 10-year annual harvest, is no longer observed when the size of the no-take reserve is 20% of the population carrying capacity. In particular, increases in reserve size to 20% or greater (i.e., 20%, 30% or 50%) further reduce both performance indicators and, hence, the probability of a complementary effect occurring. For instance, increasing the reserve size to its maximum value (s = 0.5) in conjunction with an optimal harvest strategy will, on average, reduce the NPV of fishing by 1.2% and the average 10-year harvest by 10.5%, relative to the baseline stock recovery plan. The ability of the no-take reserve to complement the optimal harvest strategy in rebuilding the depleted fishery is further illustrated in Fig. 3, which presents the mean difference over time in the total biomass (Fig. 3a), net profit of fishing (Fig. 3b), and harvest (Fig. 3c) between each of four reserve sizes (s = 0.1, 0.2, 0.3, or 0.5) and the no-reserve case (s = 0), where each is combined with the optimal harvest ( = 1). While the establishment of no-take reserves generally increases the total biomass, the difference in total biomass is in particular greater during the rebuilding period than during the period after the depleted stock is rebuilt to its target level. The figure further shows that, during the stock rebuilding period, the net profit of fishing and harvest are on average greater when 10% or 20% of the carrying capacity is placed in the reserve than when there is no reserve established. By contrast, once the fishery is rebuilt to the target level, the net profit of fishing and harvest are on average greater when the fishery is managed without the reserve for all reserve sizes examined. Fig. 3 also reinforces the results in Fig. 2 such that the complementarity between the reserve establishment and optimal harvest strategy diminishes as the reserve size further increases. For example, when 50% of

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the carrying capacity is placed in the reserve, the harvest is on average less than when the fishery is managed without the reserve for the entire period of the simulation. 4. Tradeoffs and the opportunity cost of reducing the stock rebuilding period Figs. 1 and 2 illustrate the potential for stock recovery plans, which combine both harvest control rules and no-take reserves, to generate win–win–win outcomes in terms of the conservation, economic and socio-economic performance indicators. Our simulations show that a recovery plan which combines a reserve comprising 10% of the population carrying capacity with the optimal harvest strategy has the potential to reduce the duration of the recovery period and increase both the NPV of the fishery and the 10-year annual average harvest. By contrast, for most composite recovery plans with larger reserve sizes, the potential for tradeoffs between performance indicators, particularly between the speed of stock recovery and the economic and socio-economic outcomes for the fishery, exists. When 10% of the carrying capacity is in a no-take reserve and the harvest is restricted to 60% of the optimal level ( = 0.6 and s = 0.1), the duration of the rebuilding period decreases relative to the baseline case on average by 22.6%, while both the NPV of fishing and the average harvest in the first 10 years of the rebuilding phase decline, relative to the baseline case, on average by 1.5% and 42.9%. Similarly, when the 10% reserve is established in conjunction with the slow stock rebuilding harvest strategy ( = 1.4 and s = 0.1), there is more than a 95% chance that the NPV of fishing is less than if the fishery were to be rebuilt using the baseline recovery plan. On the other hand, imposing a less restrictive harvest strategy results in an, on average, 20.1% increase in the average harvest in the first 10 years of the rebuilding phase. This socio-economic benefit is gained at the expense of the lengthened stock recovery time and the reduction in the NPV of fishing. To analyze the possible tradeoffs more explicitly, we calculate two measures of the opportunity cost of reducing the stock rebuilding period, such that: 1 M

OCNPV =

M 

NPVm ( , s) −

M 

m ( , s) −

m=1

1 10M

M 

NPVm (1, 0)

m=1

m=1 1 M

OCh10 =

1 M

M 10  

1 M

M 

m (1, 0)

m=1

ht,m ( , s) −

1 10M

m=1 t=1 1 M

(9)

M  m=1

M 10  

ht,m (1, 0)

m=1 t=1

m ( , s) −

1 M

M 

(10)

m (1, 0)

m=1

where is the number of years required to rebuild the depleted stock to its target level (i.e., xDMEY ) and M is the number of Monte Carlo samples which we set to M = 10,000 as in Section 3. The measure of opportunity cost defined in Equation (9), OCNPV , and reported in Table 2, represents the average change in the NPV of fishing per year reduction in the average recovery time. Table 3 shows the calculations of the second measure of the opportunity cost (OCh10 ), which represents the average change in the 10-year average harvest per year reduction in the average recovery time. plans which consist of different combinaBoth measures are calculated  for 25 stock recovery  tions of the reserve size (s ∈ 0, 0.1, 0.2, 0.3, 0.5 ) and the stock rebuilding harvest strategy ( ∈





0.6, 0.8, 1.0, 1.2, 1.4 ). As in Section 3, the baseline case is the recovery plan under which the fishery is managed using the optimal harvest strategy and no reserve is established ( = 1 and s = 0). We examine the economic and socio-economic cost of reducing the stock recovery time by implementing alternative stock rebuilding harvest strategies, under different assumptions about the size of the notake reserve, we report OCNPV and OCh10 for only the 16 recovery plans

for which the average duration of the rebuilding period is less than the baseline case (i.e., ¯ , s < ¯ (1, 0)). This effectively rules

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Table 2 Opportunity cost of reducing the recovery time, in million dollars. Reserve size (s)

0

0.1

0.2

0.3

0.5

1.4 1.2 1 0.8 0.6

– – Baseline case 2.259 2.597

– – −1.348 1.301 2.135

– – 0.594 1.750 2.473

– – 1.608 1.814 2.552

– 13.876 4.008 2.752 3.339

Note: The value in each cell represents the change in the net present value of fishing for each additional year of the rebuilding period reduced because of changing the reserve size and/or stock rebuilding harvest strategy. ‘–’ indicates that the opportunity cost of reducing the recovery time is not available since the average duration of the rebuilding period is greater than the baseline case. Table 3 Opportunity cost of reducing the recovery time, in thousand pounds. Reserve size (s)

0

0.1

0.2

0.3

0.5

1.4 1.2 1 0.8 0.6

– – Baseline case 1.377 1.493

– – −0.443 1.128 1.379

– – 0.125 1.198 1.414

– – 0.254 1.179 1.403

– 0.677 0.817 1.206 1.446

Note: The value in each cell represents the change in the average annual harvest for each additional year of the rebuilding period reduced because of changing the reserve size and/or stock rebuilding harvest strategy. ‘–’ indicates that the opportunity cost of reducing the recovery time is not available since the average duration of the rebuilding period is greater than the baseline case.

out all but one of the recovery plans ( = 1.2 and s = 0.5) incorporating a slow stock rebuilding harvest strategy (i.e., > 1). Negative values of OCNPV and OCh10 imply that the reduction in the duration of the rebuilding period is achieved, on average, with no resulting reduction in the economic and socio-economic fishery performance indicators. This is observed in Tables 1 and 2 for the recovery plan ( = 1 and s = 0.1) and shows the effective double-payoff of implementing the 10% reserve with the optimal harvest strategy as shown in Figs. 1 and 2, and identified above as an example of a win–win–win approach to stock recovery. For all other recovery plans that result in a reduction in the duration of the recovery period, the OCNPV and OCh10 are positive which implies there is a tradeoff between the stock rebuilding period and both the NPV of the fishery and the 10-year average annual harvest. Moreover, for recovery plans involving a given stock rebuilding harvest strategy, the establishment of a no-take reserve up to a certain size decreases the opportunity cost of reducing the recovery time according to both measures (Tables 2 and 3). This highlights the complementarity between the reserve establishment of stock rebuilding harvest strategies in terms of both the economic and socio-economic benefits for the fishery. Tables 2 and 3 show that the opportunity cost of reducing the stock recovery time differs depending on whether the cost is measured based on the economic or socio-economic outcomes of the fishery. The opportunity cost in terms of the foregone NPV of fishing (OCNPV ) is the highest when a large notake reserve (50% of the carrying capacity) is combined with a harvest in each year of the rebuilding phase that is 20% above the optimal level ( = 1.2 and s = 0.5). By contrast, the opportunity cost in terms of the average harvest in the first 10 years of the rebuilding phase (OCh10 ) is the highest for the recovery plans that restrict the harvest to 60% of the optimal level and establish no reserve (s = 0). 5. Scenario analysis The separate effects of a no-take reserve and alternative harvest strategies has been shown to depend on the value of key biological and environmental parameters (Hannesson and Steinshamn, 1991; Steinshamn, 1998; Arnason et al., 2004; Grafton et al., 2006b; Sanchirico et al., 2006, 2010;

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Yamazaki et al., 2012). To assess the effects of alternative parameter values we evaluate changes in the intrinsic population growth rate (r), the magnitude of the spillover between the reserve and harvest populations (m) and the size of a random population shock (i ) on the outcome of the fishery in terms of all three performance indicators under alternative recovery plans. We also examine the sensitivity of our results to the initial biomass condition of the fishery. To undertake the scenario analysis, we re-simulate the model to compute the three performance indicators for each of the 15 recovery plans, s ∈ {0, 0.1, 0.2, 0.3, 0.5} and ∈ {0.6, 1, 1.4}, explored in Section 3. This is done for four alternative scenarios involving, one, a slower population growth rate (r = 0.25), two, a lower transfer coefficient (m = 0.01), three, a larger negative shock on the harvest population (H = 0.5 and R = 0.13), and four, a higher initial biomass level (x0 ) corresponding to the maximum sustained yield of the fishery (xMSY = 0.5 K).16 Our purposes in this investigation is to evaluate the conservation, economic and socio-economic outcomes of alternative recovery plans for a fishery characterized by each scenario (Fig. 4) and to compare them with our earlier results for the benchmark parameterization (Figs. 1 and 2).17 Our earlier result (Section 3.1) that the establishment of a no-take reserve of up to 50% of the population carrying capacity acts as a temporal substitute for the slow rebuilding harvest strategy still holds for the scenario in which there is a reduced level of spillover (Fig. 4b) or a larger initial biomass level (Fig. 4d). By contrast, with a slower growth rate (Fig. 4a) or where the harvest population is exposed to a larger size of negative shocks (Fig. 4c) the substitution between the two rebuilding approaches becomes less pronounced. That is to say, under both of these scenarios, adoption of the slow rebuilding harvest strategy translates into only a small effect on the duration of the rebuilding period. Thus, any temporal substitution that may occur as a result of introducing a no-take reserve under the slow rebuilding harvest strategy is weaker than under the benchmark scenario. For instance, under the slow population growth scenario, setting = 1.4 in combination with a reserve of any size investigated between 0% and 50% increases the average stock rebuilding period by between 3.5% and 10.6% relative to the baseline recovery plan ( = 1.4 and s = 0). Our benchmark observation was that no-take reserves can reduce the time taken to rebuild a depleted fish stock to the target biomass level when combined with either the optimal or a slow rebuilding harvest strategy. We find this effect diminishes when either the intrinsic growth rate is low or the harvest population is exposed to a larger size of negative shocks. For instance, increasing the reserve size from 0% to 30% in a recovery plan when applying the optimal harvest strategy ( = 1) shortens the stock rebuilding period, on average, by less than 4% for both scenarios (Fig. 4a and c). The effect on the stock rebuilding period of the reserve establishment is small in these scenarios because the optimal annual harvest (h* ) is adjusted according to changes in fishery characteristics. When either the intrinsic population growth is low or the harvest population faces a larger negative shock, the harvest in each year of the rebuilding phase is set in a more conservative manner. This, in turn, makes the conservation benefit of reserve establishment weaker than in the case for the benchmark parameterization. Our result that the establishment of a no-take reserve can complement the optimal harvest strategy by improving both economic and socio-economic performance in the fishery (Section 3.2) is diminished in the low spillover or high initial biomass scenario (Fig. 4b and d). When the transfer rate of fish is low, the spillover from the reserve to harvest population cannot offset the loss in the reduced harvest population due to the increased reserve size. Similarly, the higher the initial biomass the shorter the rebuilding period and, in turn, the lower the economic and socio-economic payoffs from reserve establishment. The complementary effect is preserved and, in some cases strengthened, in the scenarios involving slow population growth (Fig. 4a) or where the harvest population is exposed to larger negative shocks

16 The third scenario is based on empirical observations that the harvest population is exposed to a greater risk of random negative effects and more vulnerable to disturbances because of fishing activities (e.g., Turner et al., 1999; Jennings et al., 2001). The same or similar specification of the negative population shocks is used elsewhere (e.g., Sumaila, 1998; Grafton et al., 2006b, 2009). For the fourth scenario, in our parameterization, xMSY is greater than the bionomic equilibrium but less than xDMEY . 17 The results for = 0.8 and 1.2 are not included in the figure to improve the clarity of the presentation. These results with = 0.8 and 1.2 are available from the authors on request.

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Fig. 4. Relative effects of increasing the reserve size and stock rebuilding harvest strategies on the rebuilding time period, NPV of fishing and 10-year average harvest for different sizes of (a) intrinsic growth rate, (b) transfer coefficient, (c) negative shocks and (d) initial biomass level. The mean ±95% confidence interval. The colored lines are quadratic fit for each . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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(Fig. 4c). For instance, in the case of a slow growing population, establishing a reserve of 10% of the population carrying capacity in conjunction with the optimal harvest strategy generates a doublepayoff with the NPV of fishing increasing on average by 0.9% and the 10-year average harvest increasing on average by 2.3%. Similarly, for the same reserve and harvest strategy, larger-sized negative random shocks to the harvest population, increases the NPV of fishing and the 10-year average harvest by 0.4% and 2.8%, respectively. This same complementarity is also evident for these scenarios in our simulations of a reserve of 10% of the population carrying capacity in recovery plans that incorporate either slow or fast rebuilding harvest strategies (Fig. 4a and c). Further, under these scenarios the complementarity, in terms of the NPV of the fishery, is extended to include a reserve of 30% of the carrying capacity. In particular, we show that under the slow population growth scenario there is more than a 95% chance that the NPV of fishing increases when 30% of the carrying capacity is placed in the reserve under the optimal harvest strategy, relative to the baseline recovery plan ( = 1 and s = 0). Fig. 4 also shows that the relative strength of the tradeoffs between performance indicators, in particular the relationship between the stock rebuilding period and economic and socio-economic outcomes of the fishery, is affected by changes in biological and environmental parameters of the fishery. For example, the ability for reserve establishment to reduce the tradeoff between the conservation and economic performance of the fishery is enhanced in the case where the population growth is lower or the harvest population faces a larger negative shock than the benchmark scenarios (Fig. 4a and c). By contrast, the potential for the reserve to complement the fast stock rebuilding harvest strategy by offsetting the reduction in the NPV of the fishery is reduced when the spillover of fish from a reserve to harvest population is low or the initial biomass is closer to the target level (Fig. 4b and d). 6. Discussion Harvest control rules and no-take marine reserves are two management approaches increasingly advocated as effective means of rebuilding depleted fish stocks and averting the collapse of fisheries. Harvest control rules reduce fishing mortality by controlling the annual catch across the fishery while no-take reserves aim to reduce mortality by prohibiting fishing across part of the fishing ground. While there is work that evaluates complementarity between no-take reserves and harvest shares (Little et al., 2010b), as far as we are aware there has been no study that quantitatively considers the performance of harvest control rules and no-take reserves when jointly used as management tools in stock recovery plans. We show that harvest control rules and no-take marine reserves can be characterized as both substitutes and complements when used together in fisheries stock recovery plans. The two management approaches can act as temporal substitutes in the sense that the length of time required for the depleted fish stock to rebuild to its target level can, in part, be mitigated through the establishment of a no-take reserve. Moreover, the mitigating effect or strength of substitution between the two approaches is stronger when the recovery plan includes a harvest control rule that aims to rebuild the stock slowly. This result is important because it suggests that a suitably designed no-take reserve may be able to offset some of the negative effects on conservation and economic values of fisheries that may arise in cases where other policy considerations, such as maintaining short-term harvest and employment, dictate the adoption of the harvest strategy of slow stock rebuilding. Our modeling demonstrates that, for each of the harvest strategies explored (i.e., optimal, fast or slow rebuilding), there is a range of reserve sizes that can act as a complement in a stock recovery plan, such that it can improve both the profitability of fishers and average annual harvest during stock rebuilding. For instance, relative to the case in which the fishery is managed with the optimal harvest strategy and no reserve is established, the recovery plan which combines a reserve comprising 10% of the population carrying capacity with the optimal harvest strategy, reduces the duration of the stock rebuilding period and increases both the NPV of the fishery and the 10-year annual average harvest. Where the 10% reserve is established, the optimal harvest strategy is adjusted to rebalance the marginal benefit and cost of fishing. Our findings complement previous results that show that the establishment of a no-take reserve can be an economically optimal strategy even when off-reserve fishing activities are optimally controlled (Brown and Roughgarden, 1997; Neubert, 2003; Janmaat, 2005; Grafton et al., 2006b, 2009; Sanchirico

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et al., 2006, 2010; Costello and Polasky, 2008; Yamazaki et al., 2010). We go further by also showing that either increasing the reserve size to 20%, 30% or 50% of the carrying capacity or deviating from the optimal harvest strategy leads to tradeoffs between the stock rebuilding period and economic and socio-economic outcomes of the fishery. Further, we demonstrate that the strength of this tradeoff varies depending on what combination of the reserve size and the harvest strategy is used in rebuilding the depleted fishery. More work is needed to further explore the role of harvest control rules and no-take reserves in rebuilding fisheries. In particular, the scope of this study does not include some key dimensions of fisheries management, including spatial dynamics of fishers’ behaviors (Holland, 2000; Smith and Wilen, 2003), non-market values of marine resources and marine reserves (Bhat, 2003), and ecosystem effects of alternative management approaches (Micheli et al., 2004). Furthermore, we select the stock rebuilding period, NPV of fishing, and 10-year average harvest to represent each of the three domains of conservation, economic and socio-economic management objectives in rebuilding fisheries. Nevertheless, increasing emphasis worldwide on the need for fisheries management to respond to a broad range of objectives highlights the importance for alternative management composite approaches to be assessed against multiple performance indicators simultaneously as done elsewhere (Péreau et al., 2012). Overall, we show that the rebuilding of depleted fish stocks may best be achieved when harvest control rules and no-take marine reserves are jointly implemented as part of stock recovery plans. Nevertheless, the complex interplay of environmental, biological and economic conditions in the fishery affects the way in which the two management approaches interact and, hence, the optimal design of such composite approaches requires careful fishery-by-fishery evaluation. Our approach and results provide a valuable step forward to improving the effectiveness of stock recovery plans in overexploited fisheries. In an environment in which the debate about the merit of marine reserves as a fisheries management tool is becoming increasingly polarized, the need for rigorous and evidence-based exploration of tradeoffs and synergies among management approaches is an imperative.

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