Simulated mark-recovery for spatial assessment of a spiny lobster (Panulirus argus) fishery

Fisheries Research 165 (2015) 42–53

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Simulated mark-recovery for spatial assessment of a spiny lobster (Panulirus argus) fishery William J. Harford ∗ , Caroline Ton, Elizabeth A. Babcock Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Cswy, Miami, FL 33149, United States

a r t i c l e

i n f o

Article history: Received 27 June 2014 Received in revised form 22 December 2014 Accepted 23 December 2014 Handling Editor A.E. Punt Keywords: Marine reserve Individual-based model Stock assessment Spatial model Tagging

a b s t r a c t Marine reserves are becoming widely implemented along with conventional fisheries controls as integrated approaches to fisheries management. The restricted spatial distribution of fishing effort, relative to the spatial distribution of fish stocks that may be partially protected by marine reserves, often necessitates spatial considerations in the design of monitoring and stock assessment. Simulation modeling was used to evaluate whether a mark-recovery design could be used to accurately estimate fishing mortality rates without information about movement rates being available to the assessment procedure. A spatiallyexplicit individual-based simulation was developed with environmental characteristics of Glover’s Reef Marine Reserve, Belize and with biological characteristics of a fished population of Caribbean spiny lobster (Panulirus argus). Accuracy of fishing mortality estimates depended on whether these estimates were calculated for the fished area only or for the entire stock. Stock-wide fishing mortality estimates could usually be obtained that were robust to uncertainty about dispersive movement. We discuss results in the context of managing fisheries based on the status of fished areas alone or on the entire stock and discuss the necessity for information about fish movement for accurate assessment of stocks managed using marine reserves. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Marine reserves have become globally popular as means to regulate fishing and non-fishing human activities within defined spatial boundaries (Lubchenco et al., 2003). In many instances, no-take marine reserves – where fishing is prohibited within reserve boundaries – are used as fisheries management tools (Botsford et al., 2003; DeMartini, 1993; Meester et al., 2004; Polacheck, 1990). This use is often coupled with other fisheries controls that together function as integrated spatial approaches to fisheries management (Hilborn et al., 2006; White et al., 2010). Stock assessment procedures are usually necessary to inform managers about how to adjust levels of fishing effort or acceptable yields in areas surrounding marine reserves. Problematically however, marine reserves complicate stock assessment and can obscure evaluations of whether fishery management objectives are being achieved (Field et al., 2006; Jennings, 2001). One reason for these complications is that marine reserves increase the spatial heterogeneity of fishing pressure by excluding harvesting over part of the fish stock’s distribution. In contrast, many stock assessment

∗ Corresponding author. Tel.: +1 305 421 4472. E-mail address: [email protected] (W.J. Harford). http://dx.doi.org/10.1016/j.fishres.2014.12.024 0165-7836/© 2015 Elsevier B.V. All rights reserved.

procedures that are used to estimate abundance and fishing mortality rates are built upon the assumption that all areas are more-or-less equally subject to fishing pressure. Consequently, whenever part of a fish stock is not vulnerable to fishing, assessment inaccuracies will occur unless this complication is addressed in data collection and assessment procedures (Beverton and Holt, 1957; McGilliard et al., 2014; Punt and Methot, 2004). Approaches have been developed that rely on the availability of fishery-independent monitoring of abundance or biomass within reserve boundaries to address spatial considerations related to assessing fisheries that are managed in conjunction with nearby marine reserves (Pincin and Wilberg, 2012; Punt and Methot, 2004). In addition, information about transfer rates between protected and fished areas are sometimes used to inform assessment models. However, assessment outcomes are known to be sensitive to the accuracy of this information (Punt et al., 2000; Punt and Methot, 2004; Quinn and Deriso, 1999). Here, we simulated a mark-recovery design not to investigate how to obtain information about movement; rather, to investigate the potential application of mark-recovery designs that are robust to fish movement uncertainty. Mark-recovery (fish tagging) has been generally useful in providing information for stock assessment, including estimation of fishing mortality rates (Hoenig et al., 1998a; Martell and Walters, 2002; Youngs and Robson, 1975). Our

W.J. Harford et al. / Fisheries Research 165 (2015) 42–53

expectation was that since individuals carry markings with them when they move, marking individuals within and around a no-take marine reserve, and with subsequent recovery by the fishery, could lead to accurate estimates of stock-wide fishing mortality without explicitly requiring knowledge about movement patterns. Simulations were constructed with spatial dimensions and environmental characteristics representative of Glover’s Reef Marine Reserve, Belize and with biological characteristics representative of a fished population of Caribbean spiny lobster (Panulirus argus). Glover’s Reef Marine Reserve includes a no-take area that covers approximately 20% of the atoll, while an economically important spiny lobster fishery occurs in the surrounding areas of the atoll (Belize Fisheries Department, 2013). Within Glover’s Reef Marine Reserve, management proceeds without information about historical yield and with limited fishery-independent sampling of relative abundance within the no-take area (Babcock et al., 2013). In addition, this spiny lobster fishery has experienced increased entry in recent years, which has led to calls for restrictions on total yield (Babcock et al., 2013; Belize Fisheries Department, 2013; Gongora, 2010). This situation is not unique to Glover’s Reef however, as fisheries for many invertebrate species, and lobster fisheries in particular, have developed rapidly in recent years (Anderson et al., 2011; FAO, 2001). Coinciding with calls for yield restriction, stock assessments of the spiny lobster fishery have already been performed without detailed information about lobster abundance within no-take areas and without information about movement between fished and no-take areas (Babcock et al., 2014; Gongora, 2010). Thus, to compare a probable baseline of assessment bias associated with the current assessment procedure for spiny lobster at Glover’s Reef with a mark-recovery-based alternative, our objectives were two-fold. We first evaluated the magnitude of bias in abundance and fishing mortality estimates that could be expected when only fishery yield and effort data were available to an assessment procedure, and the fishery operated in conjunction with a no-take marine reserve. We then evaluated whether more accurate estimates of fishing mortality could be obtained from a mark-recovery design without information about spiny lobster movement being available to the assessment procedure. Both evaluations were carried out across alternative scenarios about spiny lobster movement and spatial behavior of the fishery. Characteristics of Glover’s Reef coral atoll and its spiny lobster fishery were utilized as a strategic representation of the kinds of places where marine reserves are used to manage fisheries targeting substrate-associated fishes and invertebrates. Our simulations were not intended to directly support management decisions at Glover’s Reef. Rather, we used the simulations as a basis for discussing when information about fish movement is necessary for accurate assessment of stocks managed using marine reserves.

2. Methods 2.1. Spatially explicit simulation framework 2.1.1. Purpose The simulation framework was constructed as an individualbased model (IBM). IBMs can be used to describe the ecological movement patterns of fishes relative to management boundaries, from which patterns of connectivity, spillover, and dispersal among areas can be quantified as emergent properties (Huse, 2001; Huse and Giske, 1998; Nathan et al., 2008; Railsback et al., 1999; Werner et al., 2001). Since IBMs simulate the independent actions of many individuals, their use is intuitive for evaluating mark-recovery designs where individuals carrying marks move across landscapes

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to be later recaptured in different locations. The simulation framework is presented below according to a protocol for communicating the construction of IBMs, which is known as overview, design concepts, and details (ODD; Grimm et al., 2006). Additional details are also provided in the Appendix. 2.1.2. State variable and scales The simulation framework comprised three primary components: individual spiny lobster, the coral reef environment, and management boundaries and the fishery. All spiny lobster were considered to be adult sized and fully recruited to the fishery and comprise a single stock. In reality, whether spiny lobster at Glover’s Reef can be considered a unique stock is currently unknown, owing to uncertainty about the relative importance of localized recruitment versus long-distance dispersal of larval spiny lobster (Ehrhardt, 2005; Kough et al., 2013; Truelove et al., 2012). Nevertheless, fishery management concerns for spiny lobster persist at local, national, and international scales (Babcock et al., 2013; FAO, 2001; Gongora, 2010). Simulated individuals were characterized by location, and by whether they were carrying a unique mark assigned during mark-recovery sampling. Movement of adult spiny lobster had two forms: dispersive and migratory. Dispersive movement consisted of relocations lacking strong directionality, which occurred among the actual configuration of contiguously distributed shallow reef habitats at Glover’s Reef. Migratory movement consisted of directed relocations between shallow water and deep water habitats, which were specified in the model to occur seasonally (Childress and Jury, 2006; Herrnkind, 1980). The coral reef environment was simulated based on the actual spatial dimensions and coarse substrate characteristics of Glover’s Reef Marine Reserve, Belize. Glover’s Reef is a coral atoll located 45 km east of the coast of Belize (lat 16.82◦ N, long 87.78◦ W; Fig. 1). The isolated lagoon is enclosed by emergent reef crest and the seaward sloping forereef descends 30◦ to 45◦ downward from the surface where it connects to the vertical wall reef, which continues to depths of 400 m to 2000 m (Acosta, 2002; Acosta and Robertson, 2003; Karnauskas et al., 2011). The simulated coral reef environment consisted of (1) shallow reef habitat and (2) deep wall reef habitat. Shallow reef habitat was represented using a grid of rectangular cells with dimensions of 25 m × 25 m. This grid was created from an existing GIS layer that described the benthic geomorphology distribution of coral reefs within the lagoon and fore reefs (Mumby et al., 1995; Mumby and Harborne, 1999a,b). Shallow reef habitat consisted of 63,426 cells (each grid cell 25 m resolution; area of 625 m2 ; total area 3964 ha; Fig. 1). The deep wall reef habitat functioned as a natural refuge from fishing because its depths exceed those that are accessible by free-diving lobster fishers. The deep wall reef was not represented in a spatially explicit manner. Instead, individuals on the deep wall reef were simply aggregated separately from those in shallow habitats. The spiny lobster fishery at Glover’s Reef operates by free-diving from June 15 to February 14 of the following year, with peak fishing effort occurring at the beginning of the season (Fig. 2; Babcock et al., 2012). This temporal pattern of fishing effort was incorporated into the simulations as a representation of current fishery practices. Like other spiny lobster fisheries, catches tend to consist of newly recruited two and three year-olds, which are rapidly depleted through the fishing season (Cruz et al., 2001; Gongora, 2010; Medley and Ninnes, 1997). Commercial fishing at Glover’s Reef occurs in shallow reef habitat of the general use zone and is excluded from the neighboring area known as the conservation zone (Fig. 1). A geo-referenced GIS layer of the management zones at Glover’s Reef was provided by the Wildlife Conservation Society. Within zones, 79.8% (3164 ha) of shallow reef habitat was located within the general use zone, and 20.2% (800 ha) was located within the conservation zone. For simplicity, all shallow

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W.J. Harford et al. / Fisheries Research 165 (2015) 42–53 Table 1 Spatial dynamics scenarios describing simulated spiny lobster movement at Glover’s Reef, Belize. Scenario

Movement to/from deep wall reef?

Dispersive movement rate

No movement Reference Dispersal Increased Dispersal Deep Refuge—Reference Dispersal Mass Migration—Reference Dispersal Temporary Refuge—Reference Dispersal

No No No Yes Yes Yes

0.0 0.3 0.8 0.3 0.3 0.3

effort spatially among fishing grounds at the beginning of each week. The first approach distributed fishing effort uniformly among all fishing grounds, thus making all spiny lobster in the general use zone equally vulnerable to capture. The second approach distributed fishing effort in proportion to spiny lobster abundance, reflecting the expectation that fishers were unlikely to be uniformly distributed (Caddy, 1975; Walters et al., 1999; Walters and Bonfil, 1999). The second approach resulted in fishing grounds with higher abundance experiencing proportionally higher fishing mortality rates. 2.1.3. Process overview and scheduling Simulations were carried out using a weekly time step and each simulation consisted of a unique 35 week fishing season. During each weekly time step, model processes occurred in the following order: mortality, dispersive movement, migratory movement, and addition of new adult recruits. With the exception of recruitment, weekly processes were carried out through synchronous updating of state variables. The simulations were developed using the Java programming language and the multi-individual simulation libraries MASON and GeoMASON (Luke et al., 2005; Sullivan et al., 2013).

Fig. 1. Location of Glover’s Reef Atoll, Belize (dotted rectangle) within the western Caribbean (A), and distribution of shallow reef grid habitat (solid filled areas) within Glover’s Reef Atoll with respect to the Conservation Zone (B).

reef habitats within the general use zone were assumed to be accessible by free-diving. Overlaying the general use zone was a 1 km by 1 km rectangular grid that denoted the distribution of fishing grounds. Two approaches were specified for distributing fishing

2.1.4. Initialization Each simulation was initialized with a random seed. Prior to simulation analyses, model processes were initially run for 25 consecutive years to generate a spiny lobster population with spatial distribution among fished and unfished areas that was consistent with the specified annual fishing mortality rate. 2.1.5. Inputs Model inputs were: (1) a geo-referenced grid of shallow reef habitats, (2) a geo-referenced grid of management boundaries and fishing grounds, (3) a temporal schedule of weekly fishing effort, (4) a spatial strategy for fishing effort distribution, (5) a target annual fishing mortality rate, and (6) natural mortality rate. 2.2. Spatial dynamics scenarios

Fig. 2. Reported effort (bars) and catch-per-unit-effort (points) for the spiny lobster fishing season at Glover’s Reef Atoll. Fishing season operated from June 15th, 2011 to February 14th, 2012, totaling 35 weeks.

Alternative movement scenarios varied the probability of dispersive movement among shallow reef habitats and the magnitudes of seasonal migrations between the deep wall reef and shallow reef habitats (Table 1). In scenarios 1 through 3, no migration to the deep wall reef occurred, and thus, spiny lobster inhabited only two areas: the fished area (general use zone) and the nonfished area (conservation zone). Scenario 1 was named the No Move scenario. Scenarios 2 and 3 differed with respect to degree of dispersive movement between shallow reef grid cells and were named the Reference Dispersal scenario and the Increased Dispersal scenario, respectively. The Reference Dispersal scenario was parameterized to reflect observed movement rates reported by Acosta (2002, 1999). In the Increased Dispersal scenario, dispersal probability exceeded observed movement rates.

W.J. Harford et al. / Fisheries Research 165 (2015) 42–53

The remaining three scenarios modified the frequency and timing of movement to and from the deep wall reef. In these scenarios, a small fraction (0.03%) of newly recruiting individuals were recruited directly to the deep reef to reflect the empirical observation that some individuals of fishery recruitment age are found on the deep wall reef (Acosta and Robertson, 2003). Scenario 4 was named the Deep Refuge—Reference Dispersal scenario as spiny lobster migrated from shallow reef habitats to the deep wall reef but were not permitted to return. In this scenario, the migration probability of individuals was parameterized such that approximately 5% of the simulated stock inhabited the deep wall reef, which was calculated from an empirical comparison of spiny lobster densities between shallow reef and deep reef habitats (Acosta and Robertson, 2003). Scenario 5, the Mass Migration—Reference Dispersal scenario, reflected an autumn return to shallow reef habitats of those lobsters that had previously migrated to the deep wall reef. Specifying a return of 50% of deep-reef individuals to shallow reef habitats over a 10-week period in autumn was arbitrary, but reflected the idea that a mass return would introduce additional exploitable abundance to the fishery towards the end of the fishing season. This simulated mass return of individuals to shallow reef habitats reflected uncertainty about causes of observed increases in relative abundance that occur in the latter half of the fishing season (Fig. 2). At Glover’s Reef, observed relative abundance declines steeply during the first half of the fishing season, followed by an increasing relative abundance trend in the autumn period of the fishing season. This relative abundance increase could reflect a secondary autumn recruitment peak, movement of previously invulnerable adult spiny lobster into fished areas, or both. Mass migrations are known to occur in autumn in the Cuban spiny lobster fishery (Baisre and Cruz, 1994; Childress and Jury, 2006; Cruz and Adriano, 2001). Scenario 6, the Temporary Refuge—Reference Dispersal scenario, treated the deep wall reef as only a temporary refuge from fishing with 80% of individuals returning to shallow reef habitats during a 10-week autumn period. 2.3. Generating simulated datasets Simulation modeling consisted of generating the spatial dynamics of spiny lobster, marking of spiny lobster prior to fishing, recovery by the fishery, and the collection of fishery-dependent yield and effort information. The conditions that differed between simulations were: (a) the magnitude of the annual fishing mortality rate, (b) the fraction of the population tagged, (c) the spatial dynamics scenario, and, (d) the spatial distribution of fishing effort. Model tuning was carried out to identify effort levels that would expose individuals in the general use zone to fishing mortality equivalent to the specified natural mortality rate of 0.34 yr−1 (low mortality) and to approximately 1.5 yr−1 (high mortality). The low fishing mortality rate was chosen to represent a precautionary value and the high level was chosen to be consistent with actual estimates of fishing mortality for spiny lobster in Belize (Babcock et al., 2012; Gongora, 2010). The fraction of the population tagged ranged from 0.1% to 10%. Fishing effort was distributed uniformly across the general use zone or in proportion to spiny lobster abundance. For each combination of conditions, 100 simulated datasets were generated that consisted of 35-week fishing seasons. 2.4. Depletion modeling The DeLury depletion model is often used to assess fisheries that rapidly deplete stocks through single fishing seasons, and has been applied to spiny lobster stocks and to other invertebrate fisheries ˜ et al., 2006; Robert et al., (Babcock et al., 2013; González-Yánez 2010). The fishery-dependent data used in this assessment procedure included weekly yields and efforts. Simulated weekly yields

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(Yt ) were provided to the assessment procedure without error and weekly effort (ft ) was provided with low observation error using a coefficient of variation of 0.01. Very low observation error on fishing effort was simulated so that model outcomes would reflect bias due to spatial aspects of the simulations and not imprecise reporting of fishery-dependent data. During each week, the number of lobsters was calculated as:



ˆ t e−M/52 ˆ t+1 = N N

1−



Yt ˆt N

ˆ + t R,

(1)

ˆ t is the estimated number of lobsters at the start of week where N t, M is the annual instantaneous natural mortality rate (divided by 52 for the weekly time step), Rˆ is the total additional abundance added through the season, and t is the fraction of Rˆ that is added in each week (Robert et al., 2010).  Weekly fishing mortality rate ˆ t . A derived parameter, was approximated as Fˆt = −log 1 − Yt /N ˆF ∗ , was used to denote the cumulative fishing mortality through t

week t, which was calculated as the sum of previous weekly fishing mortality estimates. Depletion model fitting was carried out using AD Model Builder (Fournier  et al., 2012).  It was assumed that observed relative abundance Ut = Yt /ft was log-normally distributed:



ˆ t , 2 Ut ∼log normal qN



(2)

where q is a proportionality constant and  2 is residual variance. The model was fit by minimizing a concentrated negative loglikelihood function (−log ), n −log  = log 2



1 n





log

Ut

ˆ Nmid t



1 − log n



Ut

ˆ Nmid t

2 

, (3)

where q and  2 were concentrated out of the log-likelihood by specifying these parameters likelihood estimates  at their maximum  ˆ t e−M/104 1 − Yt /2N ˆt ˆ was mid-week abundance and Nmid t =N approximation used in the likelihood function (Fournier et al., 2012; Walters and Ludwig, 1994). The set of equations that was used in the assessment of stock dynamics was consistent with the manner in which stock dynamics were simulated using the individual-based framework, thus minimizing the degree of model misspecification between the simulation and assessment models. In statistical fitting, M and t were specified as known constants reflecting values ˆ 1 and Rˆ were estimated as free used in simulating the data and N parameters. Thus, fitting emphasized bias attributed to the spatial distributions of spiny lobster and its fishery rather than natural survival processes or availability of information about t . 2.5. Mark-recovery modeling The algorithm for simulated marking of spiny lobster was implemented as follows. First, a sampling grid of 100 m by 100 m rectangular cells was used to aggregate shallow reef habitats into tagging sites. Plausible tagging sites were those that contained reef habitat, which resulted in 1600 and 6223 available tagging sites within the conservation zone and general use zone, respectively. Second, the fraction of tagging sites within each zone that were visited was set to the specified fraction of the stock to be tagged. Finally, all individuals within each selected site were marked with unique identifiers. This algorithm resulted in: (1) the fraction of the population actually tagged reflecting the intended fraction to be tagged; (2) total tags being distributed in proportion to spiny lobster abundance in the general use zone and in the conservation zone; and (3) marked individuals being aggregated within tagging sites. Marking aggregations of individuals at randomly selected sites reflected a realistic sampling constraint of many

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W.J. Harford et al. / Fisheries Research 165 (2015) 42–53

mark-recovery designs (Hoenig et al., 1998b; Ley-Cooper et al., 2013; Smith et al., 2009). Marking was carried out the week prior to the opening of the fishery, and tags were retained through the fishing season. Post-release survival, tag retention rate, and tag reporting rate were all specified to be equal to 1.0. In scenarios that included migration, no tags were distributed to individuals inhabiting the deep wall reef. Fishing mortality rates were estimated from  tag-recovery data as follows. Estimation of tag recovery rates  ˆ t was based on ct cumulative returns of tagged spiny lobster through week t, from C initially tagged individuals:





ct ∼Binomial C,  ˆt .

(4)

Tag recovery rate was modeled as  ˆ t =  ˆ t,

(5)

where  is the probability of surviving the tagging process,  ˆ t is the harvest rate, and  is the tag reporting rate (Hoenig et al., 1998a; Pine et al., 2003). Harvest rate was: t =



Fˆt∗



Mt  1 − exp −Fˆt∗ −

Fˆt∗ + Mt/52

52

(6)

where Fˆt∗ Ft∗ is modeled directly as a free parameter, and t is the number of weeks since individuals were marked. In model fitting, , , and M were specified as known constants reflecting true values so that model outcomes would reflect bias and imprecision in spatial aspects of the mark-recovery design and not survival and reporting processes. The software OpenBUGS was used to estimate fishing mortality rates from simulated mark-recovery data (Lunn et al., Weekly fishing 2000).  mortalities were assigned diffuse priors Fˆt∗ ∼Uniform (0, 2) .Convergence of the Markov chain Monte Carlo (MCMC) algorithm on its target distribution was checked against Gelman–Rubin convergence criteria (Gelman et al., 2004) and was usually reached by 1000 iterations and a more conservative 2000 iterations was used as a burn-in period. Posterior samples were retained from 5000 subsequent iterations from two chains and posterior means of parameters were calculated from the resulting 10,000 saved iterations.

2.6. Performance measures Performance of assessment models was evaluated in terms of how accurately fishing mortality could be estimated for the general use zone (fished area) and for the entire stock (conservation zone + general use zone + deep wall reef). Fig. 3 provides a conceptual illustration of the spatial distribution of the simulated stock relative to the spatial area of interest for assessment. Accordingly, decision-makers could be interested in responses to management tactics within the fished area (Fig. 3A) or for the entire stock (Fig. 3B and C). In spatial dynamics scenarios that did not specify spiny lobster inhabiting the deep wall reef, the entire stock consists of the conservation zone and general use zone (Fig. 3B). The deep wall reef habitat was included in other scenarios to further emphasize emigration as an additional complexity and as a source of bias in fishing mortality estimation (Fig. 3C). For each simulation j, percent bias in fishing mortality estimates were calculated as

% biasj =

∗ − F∗ Fˆt,j t,j ∗ Ft,j

100.

(7)

Fig. 3. Conceptual illustration of fished and unfished areas used in the simulations (solid lines). Dashed lines indicate area of interest for assessment of (A) fished area only, (B) entire stock area without the added complication of additional deep water habitat, and (C) entire stock area where assessment is additionally complicated by a deep water habitat that acts as an additional refuge to harvesting.

where Fˆt∗ and Ft∗ are estimated and true cumulative fishing mortality rates, respectively. For mark-recovery models, we also calculated the precision of Fˆt∗ as a coefficient of variation (CV):

 C V t,j =

ˆ t,j ∗ Fˆt,j

(8)

where ˆ t,j is the estimated standard error of the associated fishing mortality estimate. For the depletion model, percent bias was similarly calculated   between estimated abundance at the start of ˆ 1 and (1) the true abundance in the general use fishing season N zone (fished area) and (2) the stock-wide abundance.

W.J. Harford et al. / Fisheries Research 165 (2015) 42–53

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3. Results 3.1. Spatially explicit simulation framework To better understand the simulated distribution of spiny lobster abundance, a summary is provided here and additional details are reported in the Appendix. Without movement and by imposing high fishing mortality, the conservation zone contained a disproportionally large fraction of the stock relative its areal extent (uniform fishing effort: 44%; proportional fishing effort: 47%). By the end of the fishing season, harvesting within the general use zone acted to inflate the fraction of the remaining stock that was protected within the conservation zone (uniform fishing effort: 65%; proportional fishing effort: 73%). When movement was introduced under the Deep Refuge—Reference Dispersal scenario – which was the scenario considered to be most consistent with current empirical evidence – the high fishing mortality rate that was simulated produced net migration into the fished area, thus effectively reducing the fraction of the stock contained within the conservation zone by season end (uniform fishing effort: 53%; proportional fishing effort: 67%). The simulation model was tuned to achieve target fishing mortality rates in the general use zone, but annual fishing mortality rates on the entire stock were emergent model properties that varied according to the spatial dynamics scenarios. When the model was tuned to achieve a fishing mortality rate of 1.5 yr−1 , and fishing effort was distributed equally among all fishing grounds, stock-wide fishing mortality rates for the No Movement and Deep Refuge—Reference Dispersal scenarios were 0.61 yr−1 (standard error ±0.02 yr−1 ) and 0.69 yr−1 (±0.01 yr−1 ), respectively. When effort was distributed proportional to spiny lobster abundance stock-wide fishing mortality rates for the No Movement and Deep Refuge—Reference Dispersal scenarios were 0.70 yr−1 (standard error ±0.03 yr−1 ) and 0.90 yr−1 (±0.03 yr−1 ), respectively. Stock-wide fishing mortality estimates were consistent with the expectation that as movement is increased, mixing between the fished and non-fished areas exposes a greater fraction of the stock to harvest. Spiny lobster that were initially tagged in the conservation zone, were sometimes later obtained by the fishery via movement into the general use zone. Specifying a high annual fishing mortality rate with fishing effort distributed in proportion to spiny lobster abundance, the Reference Dispersal scenario resulted in 6%, on average (range 1–12%), of the abundance within the conservation zone at the start of the season becoming captured by the fishery during the season. By increasing the dispersive movement rate in the Increased Dispersal scenario, 13%, on average (range 2–26%), of the abundance within conservation zone at the start of the season was subsequently captured by the fishery. 3.2. Depletion modeling As a baseline for comparison with the mark-recovery design, assessment bias expected when only fishery-dependent data were available, and the fishery operated in conjunction with a marine reserve, was quantified using the high fishing mortality rate of 1.5 yr−1 . For brevity, we emphasize results from the No Move, Deep Refuge—Reference Dispersal, and Temporary Refuge—Reference Dispersal scenarios to explain the effects of dispersive movement and migration on abundance and fishing mortality estimation. Starting with abundance and fishing mortality estimation within the general use zone (depicted in Fig. 3A), the No-Move scenario estimated these quantities without bias (Figs. 4 and 5A). While this result says nothing about the effect of movement, it does demonstrate that the DeLury depletion model was not misspecified relative to the dynamics simulated using the IBM. That is, without dispersive movement, the general use zone can be thought

Fig. 4. Percent bias in abundance between simulated true values and estimates from a stock assessment model for spatial dynamics scenarios 1, 4, and 6. Panel (A) is abundance bias within the fished area (i.e. the general use zone) and panel (B) is abundance bias for the entire stock (i.e. general use zone + conservation zone + deep wall reef). Results for conditions of: uniform fishing effort distribution and high fishing mortality rate.

of as being independent of the conservation zone, and thus, a correctly specified assessment model should accurately estimate fishing mortality and abundance within the general use zone. Similarly, unbiased estimates were obtained under the conditions of uniform effort distribution and when effort was distributed in proportion to abundance. The most substantial biases that arose from depletion modeling were the underestimation of stock-wide abundance and the overestimation stock-wide fishing mortality rate (Fig. 3C). Relying on fishery yield and effort resulted in a mean underestimation of stock-wide abundance by 44% for the No Move scenario (Fig. 4B). Intuitively, the magnitude of the underestimation of stock-wide abundance corresponded to the fraction of the stock that was invulnerable to fishing. When dispersal was allowed and lobster transfer between zones occurred as an emergent property of dispersive movement, bias in stock-wide abundance was still quite high, but decreased relative to the No Move scenario (Fig. 4B). As movement increased, fishery-dependent data began to contain a slightly more accurate signal about stock-wide abundance because yields reflected a slightly higher fraction of the total population. Nevertheless, this result is problematic because it demonstrates that the magnitude of bias associated with use of fishery-dependent data to assess a fishery managed in conjunction with a marine reserve

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Fig. 6. Bias (A) and coefficient of variation (CV; B) of estimated fishing mortality at four levels of tagging intensity. Values are reported at weeks 4, 17, and 35 of the 35-week fishing season under the conditions of: equal fishing effort distribution, high annual fishing mortality rate, and Reference Dispersal scenario. Parentheses contain percent of the population tagged. Fig. 5. Percent bias in annual fishing mortality rate between simulated true values and estimates from a stock assessment model for spatial dynamics scenarios 1, 4 and 6. Panel (A) is bias within the fished area (i.e. the general use zone) and panel (B) is bias for the entire stock (i.e. general use zone + conservation zone + deep wall reef). Results for conditions of: uniform fishing effort distribution and high fishing mortality rate.

is itself sensitive to the magnitude of dispersive movement rates (Figs. 4B and 5B). For instance, stock-wide fishing mortality estimates were overestimated, on average, by 98% to 148% depending on which spatial dynamics scenario was used (Fig. 5B). Compared to changes in dispersive movement rates, migration patterns to and from the deep wall reef did not have a strong influence on assessment bias in our simulations (depicted in Fig. 3C). This result occurred because the fraction of the stock inhabiting the deep wall reef was small in our simulations (approximately 5% of atoll-wide abundance), which was consistent with available empirical information about the spatial distribution of spiny lobster at Glover’s Reef. In practice though, migration can have a strong influence on the accuracy of assessment procedures, especially if emigration is incorrectly perceived as a reduction in survival. 3.3. Mark-recovery modeling In investigating the performance of mark-recovery modeling, spatial dynamics scenario 2 (Reference Dispersal scenario) was first used to evaluate the effects of the fraction of the population tagged on fishing mortality estimation. Bias and precision of fishing mortality estimates were strongly influenced by the fraction of the population tagged. Tagging extremely low fractions of the population (0.1%) considerably increased the chances of obtaining

erroneous fishing mortality estimates in any individual data realization (Fig. 6A). Marking 1% or 2% of the population considerably reduced the potential for errors. Precision of the fishing mortality estimator was also poor when only 0.1% of the population was tagged, but coefficient of variation estimates were generally <0.1 when at least 1% of population was tagged (Fig. 6B). Bias and precision patterns related to fractions of the stock tagged were consistent at both the low and high levels of annual fishing mortality. Having investigated the effects of the fraction of the population tagged on fishing mortality estimation, the remainder of the markrecovery simulations were carried out by tagging 1% of the spiny lobster stock. Stock-wide fishing mortality estimates, made without the complication of migration to/from the deep wall reef (i.e. spatial dynamics scenarios 1–3; Fig. 3B), were on average unbiased by the magnitude of dispersive movement (Fig. 7). Annual fishing mortality estimates for simulation runs with fishing effort distributed uniformly throughout the general use zone had average percent biases of 0.71% (standard error ±15.4%), 0.70% (±13.4%), and 3.1% (±14.6%) for scenarios 1, 2, and 3, respectively. When fishing effort was distributed in proportion to spiny lobster abundance, the analysis revealed a small bias in stock-wide fishing mortality estimation. Because effort was distributed proportional to abundance, some areas within the general use zone experienced higher fishing mortality rates than others. In these simulation runs, an underestimation of “true” fishing mortality occurred primarily towards the end of season. While this bias was generally small (mean: −3.9%; centered 95% of simulations: −31.4% to 40.6%), there was evidence of systematic underestimation. The mark-recovery assessment procedure used in this study assumed that all tagged and untagged individuals had equal probability of capture. This

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Fig. 7. Bias of estimated fishing mortality for three migration variants of the spatial dynamics scenarios 1 through 6. Values are reported at weeks 4, 17, and 35 of the 35-week fishing season under the conditions of: uniform fishing effort distribution, high annual fishing mortality rate, and 1% of tagging sites visited.

assumption implies that (1) tagged individuals are distributed in proportion to abundance over the population distribution, and (2) tagged individuals are caught at the same rate as untagged individuals. The latter condition was likely violated when fishing effort was not equal for all individuals in the general use zone. However, this bias was small and mark-recovery performed reasonably well at the broader objective of addressing gross stock assessment bias in the estimation of stock-wide fishing mortality. Within the weekly time steps of the simulated fishing seasons, encouraging results were also obtained. Given that at least 1% of the population was tagged, stock-wide fishing mortality estimation was reasonably unbiased and precise regardless of whether estimates were made at the start of the season (week 4), the middle of the season (week 17), or at the end of the season (week 35; Fig. 7). This finding is relevant because as the fishing season progressed, the total number of tag returns increased. It was initially unclear whether there would be sufficient tag returns near the start of the season to estimate fishing mortality, but this appears to be plausible at the levels of fishing mortality and fraction of the population tagged that were used in the simulations. Simulations that included migration to and from the deep wall reef (Fig. 3C) and simulations where fishing mortality was estimated for only within the fished area (Fig. 3A) are presented together because these two situations represent instances when survival estimation is confounded with unaccounted-for movement. When migration to and from the deep wall reef was introduced in scenarios 4 through 6, but tags were not assigned to individuals in deep wall reef, stock-wide fishing mortality estimates were biased (Fig. 7). This result occurred because individuals in the deep wall reef did not receive tags prior to fishing, and thus, migration resulted in “apparent survival” estimates that inadvertently incorporated emigration/immigration to the fished area where tag recovery occurred. This result can also be thought of as violating the closed-stock assumption associated with this type of mark-recovery design. Thus, while the mark-recovery approach we simulated appears robust to movement uncertainty, tagging in places where deep water areas serve as de facto reserves is required to avoid estimation bias. Again, in our simulations migration bias was small because only a small fraction of individuals were specified to inhabit the deep wall reef. This assumption was highly uncertain and requires additional empirical investigation. In the situation where fishing mortality estimation is desired only within fished area (i.e. Fig. 3A), marked individuals from within this area can be removed in three ways: natural mortality, fishery capture, or movement out of the fished area. Consequently, using tag recoveries from only the fished area produces biased fishing mortality unless emigration (movement out of the fished area) is accounted for. Unaccounted-for emigration produced underestimates of fished-area fishing mortality. Thus, mark-recovery

appears useful for estimating stock-wide fishing mortality without explicit knowledge of movement between areas, but biased estimates are produced if the area of interest for assessment is a smaller component of the total area within which movement occurs. 4. Discussion The DeLury depletion model simulations showed that the magnitude of bias in stock-wide estimates of abundance and fishing mortality was sensitive to rates of dispersive movement. Increased dispersive movement translated into increased spillover from reserves into fished areas. While it is intuitive to expect estimation bias to be sensitive to spillover rates, this result is problematic for stock assessment because spillover rates are often highly uncertain. Further, marine reserve design theory suggests that lowto-intermediate dispersal rates afford biodiversity protection while likely benefiting surrounding fisheries through spillover (Botsford et al., 2003; Meester et al., 2004; Sale et al., 2005). The simulations presented herein suggested that low-to-intermediate dispersal rates impose additional challenges for producing accurate stock assessments, unless either movement information is gathered for use in assessment procedures or an assessment procedure is used that is robust to movement uncertainty. Under a range of movement scenarios, accurate stock-wide fishing mortality estimation based on mark-recovery did not require knowledge about spiny lobster movement to be available to the assessment procedure. Fishing mortality rates were well approximated with 1% of the population tagged, which corresponded to 500–1000 tags for the population size range used in the simulations. Reasonable precision (CVs commonly <0.1) of fishing mortality estimates obtained from deploying several hundred tags was consistent with previous simulation studies (Frusher et al., 2001; Martell and Walters, 2002). However, fishing mortality estimates reported here were likely to be overly precise in comparison with any actual mark-recovery procedure because several parameters were fixed at their true values, rather than estimated with uncertainty from auxiliary data. Increased imprecision of fishing mortality estimates will occur when estimation uncertainty in other model parameters (e.g. reporting rate) is propagated to fishing mortality estimation within the statistical estimation procedure. Additional details on bias and precision related to design and estimation using mark-recovery methods can be found elsewhere (Pine et al., 2003; Williams et al., 2002; Youngs and Robson, 1975). In our simulations, several simplifications and assumptions were made that would need to be addressed before actually applying any mark-recovery design. Rates of tag retention, natural mortality, and tag reporting were assumed known in the simulations, but will require accurate estimation in actual

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mark-recovery designs. Empirical studies of tagging methods for lobster species suggest that tag retention can vary considerably. Since lobster growth occurs discretely in a series of molts, tag loss can occur at molting, and thus, quantifying tag retention rates will be essential for accurate fishing mortality estimation. In practice, retention rates >80% can be achieved over a single season, insertion protocols for plastic “spaghetti” tags that promote retention through successive molts have been developed, and alternative technologies such as passive integrated transponders and genetic mark-recovery techniques are available (Davis, 1978; McMahan et al., 2012; Melville-Smith and Chubb, 1997; O’Malley, 2008; Rowe and Haedrich, 2001; Taberlet et al., 1999). Another consideration includes the time and expense associated with pre-season tag distribution. As an example, the minimum number of hours it could take to mark 500–1000 individuals at Glover’s Reef was calculated using the efficiency of the commercial fishery. Babcock et al. (2013) estimated medians of 3.5 and 5.3 individuals captured per fisher hour at the beginning of the fishing seasons in 2011 and 2012, respectively. Using an average value of 4.4 would require a minimum of 113 fisher hours to tag 500 individuals. This is a minimum value because the sampling design necessitates traveling between sampling sites and because tagging and release may take considerably longer than harvesting. Nevertheless, Acosta (1999) demonstrated that spiny lobster in shallow water habitats at Glover’s Reef could be tagged by divers using either SCUBA or snorkel. Further, special care would be required to ensure fishers retain tags for reporting, especially if landings consist mainly of tails. Achieving high reporting rates often requires creative approaches to stakeholder involvement and education, which frequently include high-reward tags (Martell and Walters, 2002; Smith et al., 2009). In their review of spatial models for policy evaluation, Pelletier and Mahévas (2005) point out that spatial models are likely to be constructed under high uncertainty. Accordingly, modeling constraints should be addressed when considering how spatial simulations can most appropriately inform fisheries management policies. First, actual movement dynamics are certainly more complex than we represented in the simulations and can affect perceived performance of assessments (Bertelsen, 2013). Our simulations did not consider the effects of size-dependent and sex-dependent movement nor density-dependent movement rates ˜ et al., 2010). Further, abundance within (Follesa et al., 2009; Goni deep water remains highly uncertain, as are rates, seasonality, and inter-annual variability in migration patterns between deep and ˜ et al., 2010; Leyshallow areas (Acosta and Robertson, 2003; Goni Cooper et al., 2014). Second, natural mortality was assumed to be constant among habitats, and independent of lobster size/age and lobster density. If fished and unfished areas differed with respect to habitat quality, lobster size distribution, or density, and natural mortality also varied with some or all of these conditions, fishing mortality estimates could be biased. Third, catchability for the purposes of initial tag distribution and subsequent recovery was assumed to be equivalent among all habitats and for all individual lobster. If catchability differs among habitats or size/age, initial tag distribution could fail to meet the assumption of tag distribution in proportion to stock abundance, and thus could lead to biased fishing mortality estimates. Fourth, fishery behavior, and in particular edge effects, will often require additional study to be ˜ et al., 2010). Aggreadequately represented in simulations (Goni gation of fishing effort around reserve boundaries is sometimes directly imposed in simulations that pertain to the design of marine reserves (Kellner et al., 2007). However, in our simulations, when effort was distributed in proportion to spiny lobster abundance, effort was not highly aggregated along the edge of the conservation zone (Appendix, see Fig. A3). Despite spillover from the reserve, an edge effect did not strongly occur because patch reefs at Glover’s

Reef that are near the edge of the conservation zone are rather sparsely distributed relative to more densely aggregated forereefs and to patch reefs further north in the atoll. Whether this simulated pattern is consistent with actual fisher behavior remains unclear. In such instances of uncertainty about fishery behavior and stock dynamics, simulations should encompass a range of plausible ‘states of nature’ – represented herein by the spatial dynamics scenarios – thus, preventing results from depending too highly on particular modeling assumptions (Pelletier and Mahévas, 2005). Additionally, simulations can serve to guide future research priorities, which in turn can support re-evaluation of policy options under more informed simulations. Actual marking-based assessments can be carried out with alternative marking designs than that examined in this study, which can better support both the estimation of mortality rates and movement patterns (Bacheler et al., 2009; Fabrizio et al., 1997; Follesa et al., 2009, 2007; Hightower et al., 2001; Punt et al., 2000). Such approaches can enable basic movement patterns to be identified or enable discrimination among more detailed movement hypotheses, while also providing mortality estimates (Follesa et al., 2007). In estimating fishing mortality for a stock that experiences disparate levels of fishing pressure in different areas, decision-makers may be interested in both area-specific mortality rates and stockwide mortality rates. In places where marine reserves protect part of an exploited stock, it is sometimes unclear whether abundance within a no-take area should be incorporated into total abundance (or stock-wide fishing mortality) estimates from which acceptable harvest limitations are derived. Including abundance inside of a reserve in the total abundance calculation will generally lead to the allowance of higher fishing mortality rates in the fished area (except under stock rebuilding), which raises the question of whether such an approach is either precautionary or would lead to economically optimal outcomes (Field et al., 2006; Hilborn et al., 2006). Consequently, whether fish abundance that is protected within a no-take reserve should be treated as a separate stock component remains an open policy question (Field et al., 2006). It is thus imperative that monitoring and assessment approaches, including mark-recovery designs, can effectively detect responses to management tactics at spatial scales that are relevant to decision-making (Follesa et al., ˜ et al., 2010). For instance, in 2007; Frusher et al., 2001; Goni areas where fishing mortality is high, determining stock status that includes nearby no-take areas and the dispersal characteristics among these areas can be essential to determining the long-term performance of management practices (Bevacqua et al., 2010; LeyCooper et al., 2014, 2013). This study highlighted the need to critically consider the types and spatial extents of data that are being collected for spatial management. Through simulations, we demonstrated that mark-recovery can be a useful approach for estimating stockwide mortality estimates without information about movement between a no-take reserve and a fished area. This approach is also likely to be beneficial for in-season monitoring and yield regulation for fisheries that rapidly deplete resources through a single fishing season (Walters and Martell, 2004). Mark-recovery approaches can also be useful for assessing individual stocks within multispecies fisheries where effort targeted to any specific stock is difficult to quantify. There are of course instance where auxiliary effort information is desirable and mark-recovery approaches that incorporate this information have already been developed (Hoenig et al., 1998a). In addition to fishing mortality estimation, quantifying spillover between no-take and fished areas can be beneficial to understanding reserve contributions to surrounding fisheries. Using marking-based approaches to quantify spillover can be a more tractable approach than attempting to draw inferences about ˜ et al., 2010, reserve effectiveness from catch rate information (Goni 2006; Russ et al., 2004). More broadly, Martell and Walters (2002)

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point out that direct assessment of fishing mortality rates (via mark-recovery for instance) can help to shift policy focus away from difficulties associated with accurate abundance estimation. Fishery management is typically aimed at regulating fishing mortality, but this aim is often achieved through yield restrictions that limit excessive fishing mortality. Establishing yield limits requires knowledge of abundance or biomass, which can be difficult quantities to estimate reliably (Hilborn, 2002; Walters and Martell, 2004). Mark-recovery data can provide accurate stock-wide fishing mortality estimates without first requiring abundance estimation. But notably, yield-based controls employed along with no-take reserves have also been proposed as complementary tactics for fisheries management (Little et al., 2011). The individual-based model (IBM) that we describe in this study is an intuitive framework for exploring the effects of spatial heterogeneity in fish distribution in relation to spatial heterogeneity in the distribution of fishing effort. IBMs can enable spatially-explicit monitoring designs for spatially-structured fish populations to be evaluated before they are implemented (Pelletier and Mahévas, 2005; Thorson et al., 2012). IBMs are intuitive for modeling spatial dynamics because individual movements can be formulated based on ecological criteria and behavior, with population-level movements in relation to management or jurisdictional boundaries being an emergent model property (Börger et al., 2008; Butler et al., 2005; Dolan and Butler, 2006; Goodwin et al., 2006; Huse, 2001; Miethe et al., 2009; Railsback et al., 1999). Additionally, IBMs are useful for emphasizing individual-level biological characteristics that are otherwise difficult to incorporate in numerical approaches to policy evaluation (Bunnell and Miller, 2005; Tyler and Rose, 1994). Thus, spatially-explicit IBMs could be developed to address the effects of size-dependent, sex-dependent, and density-dependent movement rates in the development of monitoring and assessment strategies for spatial management. The flexibility of using IBMs in fisheries simulation modeling is mainly limited by the availability of supporting empirical and experimental data (Grimm and Railsback, 2005). While the use of mark-recovery for fishing mortality estimation will require investment in tag distribution, reliance on the fishery for tag recovery could be a fishery-dependent solution worth considering. Mark-recovery designs may provide solutions to spatial assessment in the face of movement uncertainty. In places where marine reserves are used as fishery management tools, data-moderate management frameworks that integrate monitoring, stock assessment and decision-making are widely needed. While information about transfer rates of adult fish between notake areas and surrounding fished areas may be available in some instances (Farmer and Ault, 2011; Ley-Cooper et al., 2014; Punt et al., 2000; Zeller and Russ, 1998), fish movement uncertainty is pervasive and can limit application of spatial approaches to stock assessment. And, fishery-independent monitoring within marine reserves may be severely limited in places that lack sufficient capacity (Mora et al., 2009; Worm et al., 2009). However, these same places may view marine reserves as important fishery management tools. Consequently, spatially-explicit fishery monitoring and assessment approaches with moderate data requirements, such as the mark-recovery approach that we examined, could be beneficial for integrating fisheries management with the use of marine reserves (Babcock and MacCall, 2011; McGilliard et al., 2011).

Acknowledgements Spiny lobster data was provided by the Wildlife Conservation Society and the Belize Fisheries Department. We thank two anonymous reviewers for their comments that led to improvement of this manuscript. Financial support for this research was

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