For Peer Review A genuine win-win: resolving the “conserve or catch” conflict in marine reserve network design Journal: Conservation Letters Manuscript ID CONL-16-0215.R2 Manuscript Type: Letters Date Submitted by the Author: n/a Complete List of Authors: Chollett, Iliana; Smithsonian Institution, Smithsonian Marine Station; University of California Davis, Coastal and Marine Sciences Institute Garavelli, Lysel; Florida Atlantic University, Harbor Branch Oceanographic Institute O'Farrell, Shay; University of California Davis, Coastal and Marine Sciences Institute Cherubin, Laurent; Florida Atlantic University, Harbor Branch Oceanographic Institute Matthews, Thomas; Florida Fish and Wildlife Conservation Comission, Florida Marine Research Institute Mumby, Peter; University of Queensland, School of Biological Sciences Box, Stephen; Smithsonian Institution, Smithsonian Marine Station Keywords: fisheries, home range, larval dispersal, no-takes, ontogenetic migration, Panulirus argus, population persistence, spatial planning Abstract: To support fishing communities, reserves should ensure the persistence of meta-populations while boosting fisheries yield. However, so far their design from the onset has rarely considered both objectives simultaneously. Here we overcome this barrier in designing a network of reserves for the Caribbean spiny lobster, a species with long larval duration for which local management is considered pointless because the benefits of protection are believed to be accrued elsewhere. Our reserve design approach uses spatially explicit population models and considers ontogenetic migration, larval and adult movement. We show that yield and persistence are negatively related, but that both objectives can be optimised simultaneously during planning. Importantly, we also show that local efforts to manage spiny lobster, the most economically valuable marine resource in the Caribbean, can result in locally accrued benefits, overcoming a major barrier to investing effort in the appropriate management of this species. Privileged Communication For Peer Review Page 1 of 41 Privileged Communication For Peer Review 1 A genuine win-win: resolving the “conserve or catch” conflict in 1 marine reserve network design 2 3 Iliana Chollett a,b,* , Lysel Garavelli c , Shay O’Farrell b , Laurent Cherubin c , Thomas R Matthews d , Peter J 4 Mumbye, Stephen J Boxa 5 6 * corresponding author. iliana.chollett@gmail.com 7 a Smithsonian Marine Station, Smithsonian Institution, Fort Pierce, FL 34949, United States. 8 boxs@si.edu 9 b Coastal and Marine Sciences Institute, University of California Davis, Davis, CA 95616, United 10 States. shay.ofarrell.ac@gmail.com 11 c Florida Atlantic University, Harbor Branch Oceanographic Institute, Fort Pierce, FL 4946, United 12 States. lgaravelli@fau.edu; lcherubin@fau.edu 13 d Florida Fish and Wildlife Conservation Commission, Florida Marine Research Institute, Marathon, 14 FL 33050, United States. tom.matthews@myfwc.com 15 e Marine Spatial Ecology Laboratory and ARC Centre of Excellence for Coral Reef Studies, School of 16 Biological Sciences, University of Queensland, Brisbane, QLD 4072, Australia. 17 p.j.mumby@uq.edu.au 18 19 Running title: Reserve networks for fisheries benefits 20 Keywords: fisheries; home range; larval dispersal; no-takes; ontogenetic migration; Panulirus argus; 21 population persistence; spatial planning 22 Type of article: letter 23 Number of words in the abstract: 145 24 Number of words in the manuscript: 2958 25 Number of references: 35 26 Number of figures: 6 27 Page 2 of 41Privileged Communication For Peer Review 2 Abstract 28 To support fishing communities, reserves should ensure the persistence of meta-populations while 29 boosting fisheries yield. However, so far their design from the onset has rarely considered both 30 objectives simultaneously. Here we overcome this barrier in designing a network of reserves for the 31 Caribbean spiny lobster, a species with long larval duration for which local management is considered 32 pointless because the benefits of protection are believed to be accrued elsewhere. Our reserve design 33 approach uses spatially explicit population models and considers ontogenetic migration, larval and 34 adult movement. We show that yield and persistence are negatively related, but that both objectives 35 can be maximised simultaneously during planning. Importantly, we also show that local efforts to 36 manage spiny lobster, the most economically valuable marine resource in the Caribbean, can result in 37 locally accrued benefits, overcoming a major barrier to investing effort in the appropriate 38 management of this species. 39 Page 3 of 41 Privileged Communication For Peer Review 3 Introduction 40 No-take marine reserves have been implemented worldwide as a conservation and fisheries 41 management strategy to prevent and/or recover from overfishing (Gaines et al. 2010). Closing areas to 42 fishing allows exploited populations to rebuild, ensuring their continued availability for future 43 generations of resource users (Roberts et al. 2001). 44 The notion of marine reserves as a fisheries management tool is dependent on two mechanisms: 45 persistence and spillover. For a population to continue to exist in the future, it needs to replace itself, 46 which is called population persistence (Hastings & Botsford 2006). In spatially structured marine 47 populations, persistence within a patch is dependent both on endogenous offspring that remain in that 48 patch and exogenous offspring that arrive from other patches. Consequently, reserves in sites with 49 higher retention and stronger connections to other reserves will have higher persistence (Fig. 1, left). 50 On the other hand, larger benefits for fisheries will be obtained when maximizing spillover, or the 51 movement of larvae and adults from reserv s to fishing grounds (Fig. 1, right). Although persistence 52 and spillover are both dependent on connectivity patterns, a reserve network that maximises either one 53 of these objectives will frequently not be the best design to maximise the other (Hastings & Botsford 54 2003; Lester et al. 2013, Fig. 1, top). 55 The awareness that marine resources are being depleted and appropriate reserve networks are needed 56 to avoid ecological collapse or even boost fisheries has mobilised a large amount of research. 57 Recently published approaches range from using heuristic guidelines on reserve size and spacing (e.g. 58 Green et al. 2014), which use the amount of area protected as a proxy for persistence; maximising 59 connectivity among units (e.g. Beger et al. 2015), which does not take persistence or yield explicitly 60 into account; including site-level metrics of connectivity (e.g. Schill et al. 2015), tackling only some 61 aspects of persistence; or maximising fisheries yield and equilibrium biomass as a proxy for 62 persistence (e.g. Rassweiler et al. 2014; Brown et al. 2015). To our knowledge, only one example has 63 focused on finding an optimal balance between yield and conservation benefits in 135 patches along 64 the Californian coast (Rassweiler et al. 2014). 65 Page 4 of 41Privileged Communication For Peer Review 4 Robust methods do exist that can simultaneously quantify both objectives, i.e. ensure the long-term 66 sustainability of the resource and benefit fisheries nearby, within a given reserve network. Spatially 67 explicit population models take into consideration the configuration of networks and the effects of 68 larval (Kaplan et al. 2006) and adult (Moffitt et al. 2009) movement to quantify persistence and 69 fisheries benefit. However, the models are so computationally intensive that they have only been used 70 to provide post hoc assessments of established reserve networks (e.g. Moffitt et al. 2009) or to select 71 among a handful of competing network configurations chosen using differing criteria (White et al. 72 2013). Despite their promise, this tool has not to date been used to design optimal reserve networks 73 from the outset within a real-world system. 74 Here we apply spatially explicit population models to the extant Honduran marine spatial planning 75 process in order to identify a reserve network configuration that will accomplish both objectives at 76 once. Our reserve design considers issues of ontogenetic migration, larval and adult movement, and 77 uses detailed spatial information on habitats and connectivity among patches. We focused on the 78 spiny lobster, Panulirus argus, which is not only the most economically valuable marine fishery in the 79 Caribbean (Cochrane & Chakalall 2001) but is also a considerable management and modelling 80 challenge as its larvae can spend up to 9 months in a pelagic stage before settling (Goldstein et al. 81 2008). We show that yield and persistence display direct trade-offs, so both objectives need to be 82 considered at the same time when planning. Additionally, contrary to what was previously thought 83 (e.g., Kough et al. 2013), a reserve network for this long-dispersing species can be beneficial at a 84 country level, which is encouraging news for conservationists and resource managers. 85 86 Methods 87 Spatially explicit population modelling approach 88 We used the dispersal per recruit model to assess the persistence and yield of reserve networks with 89 dispersing larvae and adults (Grüss et al. 2011). From an initial number of settlers, the recursive 90 population model quantifies the number of recruits, adults and eggs produced within each patch, and 91 then uses the larval connectivity matrix to link the production of eggs at one location to settlement at 92 another until reaching equilibrium (Kaplan et al. 2006, Fig. 2). The method also accounts for the 93 Page 5 of 41 Privileged Communication For Peer Review 5 movement of adults, which makes them available to fishing outside reserves therefore decreasing 94 persistence but increasing yield (Kramer & Chapman 1999). The different processes involved in the 95 model are outlined in Fig. 2 and explained in detail in the Supporting Information. 96 97 Persistence and yield - For studying the effects of spatial management on spiny lobster populations 98 the population model calculates two indices of the fishery’s state that are independent of the stock-99 recruitment relationship: eggs per recruit (EPR) and yield per recruit (YPR). EPR is the number of 100 eggs an average recruit produces over its lifetime (Goodyear 1993). Values of EPR were then used to 101 calculate the Fraction of Natural Eggs per Recruit (FNEPR). This metric is the ratio of the fished 102 (EPR) to the unfished (NEPR) reproductive potential and it is a measure of the impact of fishing on 103 the potential productivity of the population. 104 For fished populations to persist, successive generations must replace each other, increasing the value 105 of FNEPR. Generally values of FNEPR are compared against threshold levels, with 20% being 106 recommended for spiny lobsters (SEDAR 2005). Persistence was summarised using two metrics (1) 107 Perd, a dichotomous metric indicating the existence of at least one reserve with FNEPR values above 108 threshold; and (2) Perc, a continuous metric given by the sum of FNEPR values inside reserves. While 109 it has been shown that a meta-population is likely to collapse if there is not at least one population 110 with FNEPR values above threshold (e.g. Kaplan et al. 2006), the sum of FNEPR is a measure of 111 larval settlement within the network commonly used for the assessment of persistence in a spatially 112 realistic setting which allows better comparisons of competing reserve networks at similar values of 113 Perd. 114 YPR is the effect of fishing on yield, expressed in terms of the yield an average individual provides to 115 the fishery over its lifetime. YPR was calculated using the Beverton and Holt equation (Sparre & 116 Venema 1998). Yield was summarised as the total yield in the region (e.g. Kaplan et al. 2006). 117 To run the model, fishing mortality (F) outside reserves was assumed uniform (F= 0.4) and reserves 118 were considered to be effective (F=0). Initial recruitment levels were set to 1, and the model was run 119 using 13 time-steps, which were sufficient to reach equilibrium (Supporting Information). Sensitivity 120 analyses were carried out to assess the effects of model parameters on the results, showing that the 121 Page 6 of 41Privileged Communication For Peer Review 6 choice of a near-optimal reserve network is insensitive to the values used (Supporting Information). 122 The implementation of the dispersal per recruit model was heavily reliant on the functions of the R 123 package ConnMatTools (Andrello 2014). 124 Trade-offs 125 A near-optimal network of reserves was identified as the one that would maximise conservation (Perc) 126 and fisheries (Yield) benefits. We consider near-optimal solutions given that the solution does not 127 necessarily represent the global optima, which might be intractable in many real-world problems 128 using heuristic algorithms (Pressey et al. 1996). Our near-optimal solution reflects the point where the 129 rate of improvement of the objective function decreases considerably (Supporting Information). To 130 that end we first calculated the minimum and maximum possible values for Perc and Yield by running 131 100 optimisations for each value (i.e. 4 separate analyses). Then, for each network configuration, we 132 used these ranges to normalize Perc and Yield values, and finally quantify our objective function (OF) 133 as the square root of the sum of squared differences between the normalized values and the ideal 134 optimum of 1. The OF weights both objectives equally and ranges between 0 and √2 (1.4142), with 135 lower values being more desirable. Networks with populations that would collapse (Perd=0) were 136 penalized and assigned a value of √2. 137 Optimisation 138 A genetic algorithm (Moilanen et al. 2009) was used to identify the network configuration that 139 optimises yield and persistence. The optimisation was based on the method kofnGA in the R package 140 of the same name, a genetic algorithm for subset selection that minimises a user-defined objective 141 function for that subset (Wolters 2015). Each run was carried out 300 iterations, and the whole 142 process was repeated 300 times (details on the method and sensitivity analyses in Supporting 143 Information). The genetic algorithm was run as an array in Hydra, the Smithsonian Institution High 144 Performance Cluster (SI/HPC). Each of the 300 runs took about 512Mb of memory and one day of 145 computing time. Hydra was able to complete all runs in less than two days. 146 Case study 147 Page 7 of 41 Privileged Communication For Peer Review 7 Eastern Honduras holds 93% of the shallow consolidated habitats and 92% of industrial fishing effort 148 in the country with spiny lobster being the most important fishery in terms of effort (Chollett et al. 149 2016) and profits (FAO 2015). The country-wide governmental target in Honduras is to fully protect 150 20% of habitats from fishing, the only use in the area (Fig. 3). 151 For species such as spiny lobsters that undertake ontogenetic migration, reserves succeed only if 152 established in each of the habitats used at different stages: (1) lagoonal and back-reef areas where 153 lobsters recruit and juveniles forage, (2) fore-reefs which adults inhabit and (3) deeper regions where 154 adults reproduce. Reserves were placed only if all three zones needed for spiny lobster were within 155 reach. This is, management units were considered in the analyses only if at least 5 km 2 of each zone 156 was available within 100 km2 of continuous habitat. Four datasets were produced as inputs for this 157 study: (1) a map of geographic zones classified from Landsat satellite imagery; (2) a three-year larval 158 connectivity matrix encompassing the entire Caribbean basin with a spatial resolution 18 times that of 159 previous datasets (Kough et al. 2013); (3) an adult connectivity matrix considering daily and nomadic 160 movements for lobster; (4) a synthesis of published population parameters for spiny lobster. All 161 datasets are described in the Supporting Information. 162 Before identifying the best network configuration for the study area, we assessed the three following 163 questions related to the general approach. (1) Can the management for spiny lobsters at country level 164 produce conservation benefits; (2) Will management be effective if fishing intensity increases?; (3) 165 What is the nature of the trade-offs between yield and persistence? To assess these questions, we ran 166 the population model for 100 reserve networks randomly distributed over the management units while 167 varying two parameters, the proportion of area protected (from 0 to 100% at 5% intervals) and fishing 168 mortality (F, from 0 to 2 at 0.1 intervals). 169 170 Results 171 Can the management for spiny lobsters at country level produce conservation benefits? 172 Both metrics of persistence (Perd and Perc) increase with increasing amount of area protected in 173 Honduras (Fig. 4A, 4B). Populations always collapse (Perd = 0) under no protection and reserve 174 networks never collapse when protecting at least 20% of the area (Fig. 4A). Serendipitously, this 20% 175 Page 8 of 41Privileged Communication For Peer Review 8 cut-off coincides with the governmental target of protection imposed in the country. Yield decreases 176 almost linearly with increasing amount of area protected, as fewer areas are available to fishing (Fig. 177 4C). 178 Will management be effective if fishing intensity increases? 179 When protecting 20% of the region, both metrics of persistence decrease with fishing pressure (Fig. 180 4D, 4E). Population collapse is possible if F ≥ 0.5, and it always occurs if F ≥ 1 (Fig. 4D). The 181 relationship between fishing mortality and yield is more complex (Fig. 4F). Yield increases with 182 fishing mortality up to a maximum around values of F of 0.3, after which populations are not able to 183 replenish themselves and yield decreases steadily with further increases in fishing. 184 What is the nature of the trade-offs between yield and persistence? 185 Interestingly, the nature of the trade-off between yield and Perc (Fig. 5) varies with the level of fishing 186 mortality when protecting 20% of the region. At low values of F these variables show direct trade-187 offs, and reserve networks that increase yield result in a proportional decrease of persistence and vice 188 versa. At high values of F the relationship becomes less steep, and at very high values of F (bottom 189 left of Fig. 5) the relationship is inverted, with high yield obtained in networks that also provide high 190 persistence. 191 Near-optimal network configuration 192 The genetic algorithm found solutions with varied spatial configurations that achieved similarly high 193 levels of yield and persistence, indicating that there are many viable spatial options for achieving both 194 goals. Although there is large variability among results, some locations are key and are always 195 selected by the algorithm (Fig. 6A). The near-optimal solution is presented in Fig. 6B. 196 197 Discussion 198 By leveraging advances in cluster computing and biophysical modelling, we were able to design a 199 reserve network to sustain the fishery of a demographically complex and commercially important 200 species at a country level. 201 Successfully managing spiny lobster fisheries at a country level is possible. Our results show that 202 populations always collapse when no protection is in place and that reserves located in Honduras can 203 Page 9 of 41 Privileged Communication For Peer Review 9 directly benefit the lobster populations of the country itself. This result challenges the perception that 204 because of their long larval pelagic duration, spiny lobster populations are unmanageable or 205 necessarily require international cooperation for effective management (Kough et al. 2013), 206 overcoming a major barrier to investing local effort in the management of this marine species. The 207 relative importance of within-country vs. international management would be dependent on country-208 level patterns of population persistence, which must be assessed to identify which strategy is most 209 likely to be effective. 210 The proposed network of reserves protecting 20% of the fishable area might not be enough to avoid 211 the collapse of the resource in the face of increasing fishing effort. Therefore, the long-term benefits 212 of the proposed network of reserves are contingent on complementary management strategies that 213 regulate fishing effort (Roberts 1997). 214 Yield and persistence show direct negative trade-offs, therefore both variables need to be considered 215 explicitly and simultaneously when planning for fisheries and conservation benefits. Rassweiler et al. 216 (2014) found similar results when planning in California. An interesting contribution of our research, 217 however, is that the nature of this trade-off can change if the resource is on the verge of collapse. 218 Recent marine spatial planning attempts that maximise only one benefit at a time (e.g. Brown et al. 219 2015; Schill et al. 2015) might produce perverse outcomes. 220 The approach presented here is transferable to other species and regions (as long as population 221 parameters and connectivity data are available), and can be extended to consider more complex case 222 studies that trade off multiple objectives (by modifying the objective function). Presently marine 223 spatial planning is dominated by the use of a decision support tool (Marxan: Ball & Possingham 224 2000) that requires the use of static information on connectivity (Beger et al. 2010). It has been shown 225 that incorporating connectivity information in static planning is sub-optimal in the sense that it does 226 not capture conservation benefits or persistence of all species under all settings (Costello et al. 2010; 227 White et al. 2014; Brown et al. 2015). We hope that by showing it is possible to explicitly include 228 population persistence during planning, we will promote the use of more comprehensive approaches 229 in future efforts for designing reserve networks when benefiting fisheries is the main objective of the 230 design. 231 Page 10 of 41Privileged Communication For Peer Review 10 The knowledge that local management actions can accrue benefits within the country is a powerful 232 motivation for the development of a network of reserves and new policies in Honduras. Currently, 233 local stakeholders are pushing for a change in socially and ecologically unsustainable methods of 234 fishing (based on dangerous scuba diving: Harborne et al. 2001). The establishment of a network of 235 reserves, linked to the development of artisanal skin-dive fisheries and the setting up of artificial 236 shelters in fishing grounds that receive spillover (Baine & Side 2003) would facilitate the transition 237 towards better ways of fishing. Within a broader regional context, the knowledge that reserve 238 networks can promote the sustainability of the resource could complement the management of spiny 239 lobster from traditional tools based on seasonal bans and size restrictions (Seijo 2007) with the 240 inclusion of networks of reserves encompassing the entire Mesoamerican region, a process that is 241 currently underway and to which the authors are contributing. 242 This study uses existing tools combined with new information and technology to provide a spatial 243 conservation support tool with direct application for the key fisheries in the Caribbean. Our approach 244 has overcome two research barriers, showing that marine reserves can be designed from scratch to 245 provide both, short-term fisheries income and long-term sustainability of the fisheries resources, and 246 that marine reserve networks can promote the sustainability of spiny lobster. We anticipate these 247 methods can support effective fisheries management and policy formation in other regions. 248 249 Acknowledgements: IC and SJB are supported by the Summit Foundation. Research leading to this 250 publication received Federal funds under award NA15NMF4690391 from NOAA Fisheries 251 Headquarters Program Office, U.S. Department of Commerce. SOF is funded by NSF Coastal SEES 252 program grant 1325452. PJM is funded by ARC Linkage and Centre of Excellence grants. Thanks to 253 Lotte Purkis for mapping the uncharted reefs of eastern Honduras for the first time, and to David 254 Kaplan and Loo Botsford for discussions on some of the topics of the manuscript. 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The value of larval connectivity 336 information in the static optimization of marine reserve design. Conserv. Lett., 7, 533–544. 337 Wolters, M.A. (2015). A genetic algorithm for selection of fixed-size subsets with application to 338 design problems. J. Stat. Softw. Code Snippets, 68, 1–18. 339 340 341 Page 14 of 41Privileged Communication For Peer Review 14 Figure Legends 342 343 Figure 1. Competing designs for a network of two reserves with the highest (upper panels) and lowest 344 (lower panels) persistence and spillover. Reserves are depicted in black, fishing grounds in grey. 345 Arrows indicate the direction of export of larvae and/or adults. Black arrows highlight the relevant 346 connections to assess either persistence or spillover. The optimal design is highly dependent on the 347 particular connectivity patterns. In this example, the worst configuration for either persistence or 348 spillover is the same, namely protecting poorly connected sites. However, the network that allows the 349 highest persistence protects sites that export mostly to one another, but the network that allows the 350 highest spillover protects sites that export mostly to fished sites. An optimal reserve design for 351 fisheries management must balance these conflicting objectives. 352 353 Figure 2. Summary of the modelling approach. For each potential reserve network, a spatially explicit 354 population model encompassing the processes of density-dependent survival of settlers (hockey-stick 355 function with slope at the origin calculated using a critical Fraction of Natural Eggs per Recruit of 0.2 356 and the correction suggested by White (2010)), adult survival incorporating both natural and fishing 357 mortality that accounts for exposure due to adult movement (Goodyear 1993), fecundity (given by 358 known fecundity at length relationship including multiple broods) and larval settlement, was run for 359 13 time-steps to calculate persistence and yield. A genetic optimisation algorithm was run for 300 360 iterations to identify network configurations that optimise both persistence and yield, subject to the 361 condition that at least one reserve has values of Fraction of Natural Eggs per Recruit above threshold. 362 The whole process was repeated 300 times and the best solution was chosen. 363 364 Figure 3. Map of the study area. Area of interest in Honduras, geographic zones and the 1,211 365 management units of 25 km2 in the area distributed along almost 25,000 km2 of shallow habitats in the 366 Miskitu cays and the Eastern banks, where the Honduran government requires the protection of 20% 367 of shallow consolidated habitats in a stratified way. 368 369 Page 15 of 41 Privileged Communication For Peer Review 15 Figure 4. Influence of area protected and fishing mortality on persistence and yield. Changes in Perd 370 (A, D), average Perc per management unit inside reserves (B, E) and average yield per management 371 unit outside reserves (C, F) at different values of area protected (A, B, C) and fishing mortality (D, E, 372 F). Variability indicates the range of outcomes after running the population model in 100 reserve 373 networks. In boxplots, lines represent the median, boxes the 25th and 75th percentiles and whiskers 374 the extremes of the data (median ± 1.5 * interquartile range). Yield indicates the average yield (g) an 375 individual lobster contributes to the fishery over its lifetime. Grey bars indicate the percentage of area 376 protected (20%) and level of fishing mortality (0.4) used in subsequent analyses. 377 378 Figure 5. Trade-offs between yield and persistence when protecting 20% of the region. Trade-offs 379 between yield and Perc for 100 random reserve networks at different values of fishing mortality 380 between 0 and 2 (annotated in the figure). Yield and persistence are expressed per management unit. 381 Colours indicate differences in Perd: black indicates when none of the networks collapse (i.e., there is 382 always at least one reserve with FNEPR > 0.2), red indicates when all networks collapse, yellow 383 indicates when results are mixed. 384 385 Figure 6. Selecting reserve networks in Honduras. Frequency of selection of 300 solutions (A); and 386 best solution (B) 387 Page 16 of 41Privileged Communication For Peer Review Figure 1. Competing designs for a network of two reserves with the highest (upper panels) and lowest (lower panels) persistence and spillover. Reserves are depicted in black, fishing grounds in grey. Arrows indicate the direction of export of larvae and/or adults. Black arrows highlight the relevant connections to assess either persistence or spillover. The optimal design is highly dependent on the particular connectivity patterns. In this example, the worst configuration for either persistence or spillover is the same, namely protecting poorly connected sites. However, the network that allows the highest persistence protects sites that export mostly to one another, but the network that allows the highest spillover protects sites that export mostly to fished sites. An optimal reserve design for fisheries management must balance these conflicting objectives. 178x102mm (300 x 300 DPI) Page 17 of 41 Privileged Communication For Peer Review Figure 2. Summary of the modelling approach. For each potential reserve network, a spatially explicit population model encompassing the processes of density-dependent survival of settlers (hockey-stick function with slope at the origin calculated using a critical Fraction of Natural Eggs per Recruit of 0.2 and the correction suggested by White (2010)), adult survival incorporating both natural and fishing mortality that accounts for exposure due to adult movement (Goodyear 1993), fecundity (given by known fecundity at length relationship including multiple broods) and larval settlement, was run for 13 time-steps to calculate persistence and yield. A genetic optimisation algorithm was run for 300 iterations to identify network configurations that optimise both persistence and yield, subject to the condition that at least one reserve has values of Fraction of Natural Eggs per Recruit above threshold. The whole process was repeated 300 times and the best solution was chosen. 197x89mm (300 x 300 DPI) Page 18 of 41Privileged Communication For Peer Review Figure 3. Map of the study area. Area of interest in Honduras, geographic zones and the 1,211 management units of 25 km2 in the area distributed along almost 25,000 km2 of shallow habitats in the Miskitu cays and the Eastern banks, where the Honduran government requires the protection of 20% of shallow consolidated habitats in a stratified way. Fig. 3 139x75mm (300 x 300 DPI) Page 19 of 41 Privileged Communication For Peer Review Figure 4. Influence of area protected and fishing mortality on persistence and yield. Changes in Perd (A, D), average Perc per management unit inside reserves (B, E) and average yield per management unit outside reserves (C, F) at different values of area protected (A, B, C) and fishing mortality (D, E, F). Variability indicates the range of outcomes after running the population model in 100 reserve networks. In boxplots, lines represent the median, boxes the 25th and 75th percentiles and whiskers the extremes of the data (median ± 1.5 * interquartile range). Yield indicates the average yield (g) an individual lobster contributes to the fishery over its lifetime. Grey bars indicate the percentage of area protected (20%) and level of fishing mortality (0.4) used in subsequent analyses. 551x567mm (600 x 600 DPI) Page 20 of 41Privileged Communication For Peer Review Figure 5. Trade-offs between yield and persistence when protecting 20% of the region. Trade-offs between yield and Perc for 100 random reserve networks at different values of fishing mortality between 0 and 2 (annotated in the figure). Yield and persistence are expressed per management unit. Colours indicate differences in Perd: black indicates when none of the networks collapse (i.e., there is always at least one reserve with FNEPR > 0.2), red indicates when all networks collapse, yellow indicates when results are mixed. 202x149mm (300 x 300 DPI) Page 21 of 41 Privileged Communication For Peer Review Figure 6. Selecting reserve networks in Honduras. Frequency of selection of 300 solutions (A); and best solution (B). 281x293mm (300 x 300 DPI) Page 22 of 41Privileged Communication For Peer Review 1 Supporting Information A genuine win-win: resolving the “conserve or catch” conflict in fisheries reserve network design Iliana Chollett, Lysel Garavelli, Shay O’Farrell, Laurent Cherubin, Thomas R Matthews, Peter J Mumby, Stephen J Box Index 1. Spatially explicit population model: Detail 2 2. Spatially explicit population model: Sensitivity analyses 4 3. Genetic optimisation: Detail 6 4. Genetic optimisation: Sensitivity analyses 7 5. Data sources: Map of zones 9 6. Data sources: Larval connectivity matrix 11 7. Data sources: Adult connectivity matrix 12 8. Data sources: Lobster parameters 14 References 18 Page 23 of 41 Privileged Communication For Peer Review 2 1. Spatially explicit population model: Detail In this section we present in detail the different processes involved in the spatially explicit population model introduced in the methods section (Grüss et al. 2011). Density dependence –To calculate the number of recruits from the number of settlers we used a hockey-stick recruitment function (Barrowman & Myers 2000), which describes appropriately density-dependent recruitment in benthic invertebrates with limited post-settlement habitat (Wahle & Steneck 1991; Kaplan et al. 2006). The slope at the origin of the egg-recruitment curve was calculated using a critical Fraction of Natural Eggs per Recruit (a measure of the impact of fishing on the potential productivity of the stock) of 0.2 (SEDAR 2005) and the correction suggested by White (2010) which accounts for processes spanning the egg-recruit transition that are characteristics of a spatial population. Survival - Adults are subjected to natural and fishing mortality (Eq. 1). The survival of individuals at different ages (la) was calculated using the relationship given by Goodyear (1993, Eq. 1), which incorporates both natural mortality (M) and the instantaneous fishing mortality rate which accounts for exposure due to adult movement (F*) when individuals are older than the age at first capture (tc).  =    <  ∗ ≥ Eq. 1 Fecundity - Due to the difficulty of aging lobsters, most population parameters for the species have been calculated using length, particularly the length of the carapace (CL). Therefore, we used known relationships between CL and age a (von Bertalanffy growth, Eq. 2), and between egg production (EP) and CL (Eq. 3), to estimate egg production at a given age. Continuous values were discretised to the mean value for each age category. K, L∞ and t0 are the von Bertalanffy parameters for, respectively, growth rate, asymptotic length (mm) and age at which individual would be length 0 (yr). α and β are parameters for the fecundity-at-length relationship. CLa = L∞ (1 - exp -K (a-t0)) Eq. 2 EPa = α CLa 2- β Eq. 3 Large spiny lobster females produce several broods per year (Briones-Fourzán, 2014). Therefore, fecundity at age (fa) was quantified by multiplying the number of eggs by the number of broods produced that year (b, Eq. 4). fa = EPa b Eq. 4 Settlement - Using the fecundity values and the spatially explicit larval connectivity information we were able to estimate the number of settlers arriving at each site in the next time-step (Kaplan et al. 2006). Persistence and yield - For studying the effects of spatial management on spiny lobster populations the spatially explicit population model calculates two indices of the fishery’s state that are independent of the stock-recruitment relationship: eggs per recruit (EPR) and yield per recruit (YPR). EPR is the number of eggs an average recruit produces over its lifetime, which approximates to the spawning stock biomass per recruit. EPR was calculated by considering fecundity (fa) and survival (la) for all ages using Eq. 5 (Goodyear, 1993).  = ∑  Eq. 5 Values of EPR were then used to calculate the Fraction of Natural Eggs per Recruit (FNEPR). This metric is the ratio of the fished (EPR) to the unfished (NEPR) reproductive potential and it is a measure of the impact of fishing on the potential productivity of the population (Eq. 6).  =  Eq.6 Page 24 of 41Privileged Communication For Peer Review 3 With NEPR being quantified as in Eq. 5, and survival calculated without the influence of fishing mortality (Eq. 7):  =  Eq. 7 YPR is the effect of fishing on yield, expressed in terms of the yield an average individual provides to the fishery over its lifetime. YPR was calculated using the Beverton and Holt equation (Sparre and Venema, 1998):  =   !"!#∑ [%&&' !"!(/  + + + ,-]/&01 Eq. 8 Where W∞ is the mean asymptotic weight calculated from L∞ and the weight-at-length relationship showed in Eq. 9, with tr as the age at recruitment, with U=[1,-3,3,-1].  = 2345 Eq. 9 Trade-offs - An optimal network of reserves was identified as the one that would maximise as much as possible both the benefit to fisheries (i.e. Yield) and persistence (i.e. Perc). To that end, we first normalized Yield and Perc values using their known minimum and maximum (Eq. 10, 11): ,6 = 78"  9:&78"9;78"  9:&78" Eq. 10 ,<= = >:7?@  9:&>:7?@9;>:7?@  9:&>:7?@ Eq. 11 Minimum and maximum persistence and yield values were obtained by running 100 optimisations for each parameter. Dimensionless, normalized values (nPerc and nYield) were then used to build the objective function (OF) that minimises the square root of the sum of squared distances of individual observations from their known optimal, in this case for normalized values, 1 (Eq. 12). The procedure described in Eq. 12 is what Branke et al. (2008) called a global criterion method in L2 or Euclidean norm. A = B 1 − ,6 E + 1 − ,<=E Eq. 12 This “no-preference” unweighted method was used to find a compromise solution that was as close as possible to optimal (maximum) values of yield and persistence. Page 25 of 41 Privileged Communication For Peer Review 4 2. Spatially explicit population model: Sensitivity analyses Equilibrium Simulations were considered to have reached equilibrium if the slopes of the regression lines fit to the 10 most recent normalized (between 0 and 1) values of each state were all less than 0.001 in absolute value (Caswell and Etter 1993). Equilibrium was invariably reached at 11 iterations, both for yield and number of settlers, when assessing 100 networks for 100 time-steps. Therefore, in subsequent analyses, all runs were iterated for 13 time-steps. Parameters The influence of each parameter in total yield and persistence (sum of FNEPR within the reserve or Perc) was tested one at the time. Unless noted, parameters were varied ±10% their default value (Table S8.I). To compare patterns of yield and persistence we ran the spatially explicit population model using the same 100 random reserve networks, each covering 20% of the targeted area. After each model run we quantified: (1) The percentage change between average yield and persistence obtained with the default parameter and the alternative. (2) The pair-wise dissimilarity (calculated as 1-Pearson correlation coefficient) between the values of yield and persistence obtained with the default parameter and the alternative. Although comparing absolute values is the most common approach during sensitivity analyses, the second metric is more informative to our aim of identifying parameters that prevent ranking reserve networks in a consistent manner. All outputs are highly correlated and dissimilarities are very small (Figure S2.1C, D). This indicates that the same networks always have the largest (or the smallest) values for yield and persistence. Therefore, the process of comparing, ranking, and choosing an optimal network is largely insensitive to the population parameters included within the model. The parameters, however, do influence absolute changes in yield, and to a lesser degree, persistence (Figure S2.1A, B). Fishing mortality (F) has the largest influence on persistence. The critical value of FNEP (critFNEP, or the slope at the origin of the egg-recruitment curve) and one of the parameters of the weight-at- length relationship (∆) are the most important factors determining yield. Page 26 of 41Privileged Communication For Peer Review 5 Figure S2.1. Sensitivity of persistence within the reserve and total fisheries yield to model parameters. (A) Percentage change in average persistence; (B) Percentage change in average yield; (C) dissimilarity (1-R) between outputs for persistence; (D) dissimilarity between outputs for yield. We assessed the parameters listed in Table SIII with two additions: the critical FNEP used to calculate the slope at the origin of the egg-recruitment curve (critFNEP), and ‘mobility’, or the effect of including adult spillover in our results, by comparing our default results with the ones obtained assuming sedentary adults. Parameters were assessed considering variation of -10% (grey) and +10% (black) around the default value with the exception of parameters that are known to vary more wildly: tr (assessed at ages of 1 and 3), tc (assessed at ages of 1.45, 3.45), F (assessed at values of 0.2, 0.4), b (with 1 or 3 broods), critFNEP (assessed at values of 0.1, 0.3). Page 27 of 41 Privileged Communication For Peer Review 6 3. Genetic optimisation: Detail The reserve design network problem involves choosing the best subset of k reserves from n candidate sites, which is a combination problem that in our case has 10,261 subsets to choose from. Because the number of possibilities is large enough to make exhaustive search impractical, efficient optimisation was needed to solve our problem. Several optimisation techniques allow searching solutions spaces with multiple local optima, with simulated annealing and genetic algorithms being the most commonly used in spatial planning (Moilanen et al. 2009). Genetic algorithms are common optimisation techniques that improve a population of possible solutions through generations using principles of evolution such as natural selection, crossover and mutation. In a genetic algorithm an initial population (a set of candidate solutions) is chosen at random, and its fitness is determined by the objective function value. In each generation, a proportion of the population gets to reproduce with a frequency that is proportional to its fitness. During reproduction, two parents (selected at random) are combined in crossover, where a new child is generated containing properties of both parents, with some mutations allowed. In the next step, the new solutions generated by the process of crossover and mutation are included in the next population, their fitness calculated, and then the population of the next generation will be selected from this augmented population. During the process, some solutions with better fitness, called elite, will enter directly in the new generation, while the other will be randomly chosen. This way good solutions with high fitness get to reproduce more frequently. To apply the genetic optimisation, we used the method kofnGA, a genetic algorithm for subset selection that minimizes a user-defined objective function for that subset (Wolters 2015). The method includes five parameters: the initial population size, the tourney size, the mutation probability, the percentage of fit solutions to keep and the number of generations to run (Table S3.I). Table S3.I. Parameters included in the genetic optimisation process, description, default value used during the runs and implications of changing the value. Parameter Description Value Implications popsize Initial population size. A set of candidate solutions 200 Larger values tend to improve the diversity of the search with a computational cost tourneysize Tourney size. The selection of mating pairs is done by tournament selection based on ranks, where two groups of solutions including tourneysize of popsize are selected at random, compared, and a victor is chosen based on ranks 10% popsize Smaller values will promote a better search of the solution space while reducing the convergence rate mutprob Mutation probability. Crossover between victors occurs by selecting indices of the two parent vectors uniformly at random. Each element has a fixed probability of mutprob of undergoing mutation 0.01 Higher values will promote exploration of the search space while reducing the convergence rate keepbest Percentage of fit solutions to keep. New populations are formed by combining the keepbest most fit solutions from the old generation with the new offspring 10% popsize Smaller values will promote diversity while reducing the convergence rate ngen Number of generations to run. The process is carried out ngen times 300 Larger values will favour equilibrium conditions Page 28 of 41Privileged Communication For Peer Review 7 4. Genetic optimisation: Sensitivity analyses Equilibrium As in section 2, simulations were considered to have reached equilibrium if the slopes of the regression lines fit to the 50 most recent normalized (between 0 and 1) values of the objective function were all less than 0.001 in absolute value (Caswell and Etter 1993). Equilibrium was reached between 64 and 145 iterations when assessing 20 runs for 500 generations. This indicates that the value used for all analyses of 300 generations was sufficient to assess equilibrium conditions in the optimisation process. It is important to note, however, that although in small amounts (the difference between values at generation 500 and 300 had a median of 0.05), the solutions kept improving when increasing the number of generations (Figure S4.1). For future work it would be interesting to compare this and alternative optimisation algorithms (e.g. simulated annealing) in terms of convergence rate and speed, in order to implement the spatially explicit population model using the best optimisation available. Figure S4.1. Values of (A) normalized Objective Function (OF); and (B) rate of change in this value when increasing the number of generations in the optimisation procedure. Black lines indicate each of 20 runs, red line the average of all runs. Parameters We used the default values defined by Wolters (2015) within the optimisation framework. To assess the sensitivity of the genetic algorithm to the specific choice of parameter values, the influence of each optimisation parameter in the value of the objective function, normalized persistence and yield was tested one at the time, as in section 2. To compare patterns, we ran the optimisation algorithm 20 times and quantified the percentage change obtained with the default parameter and the alternative. Pair-wise dissimilarities could not be calculated because the optimisation method initiates each run with random conditions. The results are highly insensitive to the choice of optimisation parameters (Figure S4.2). The objective function (OF) is the least sensitive to the choice of parameters, and values of OF vary less than 1% when optimisation parameters are changed. Relatively, persistence (Perc) is the most sensitive variable to the choice of parameters, however, maximum deviations are less than 3% from the baseline. The mutation probability (mutprob) and the percentage of fit solutions to keep (keepbest) had the largest influence in the results. A B Page 29 of 41 Privileged Communication For Peer Review 8 Figure S4.2. Sensitivity of the outputs to optimisation parameters. (A) Percentage change in average value for the objective function; (B) Percentage change in average normalized persistence; (C) Percentage change in average normalized yield. We assessed the parameters listed in Table S3.I. Parameters were assessed considering positive (black) and negative (grey) variation around the default value. popsize (assessed at 100 and 300), tourneysize (assessed at 5 and 15%), mutprob (assessed at values of 0.001 and 0.05), keepbest (assessed at 5 and 15%). -10 -5 0 5 10 popsize tourneysize mutprob keepbest Change in yield (%) -10 -5 0 5 10 popsize tourneysize mutprob keepbest Change in persistence (%) -10 -5 0 5 10 popsize tourneysize mutprob keepbest Change in OF (%) A B C Page 30 of 41Privileged Communication For Peer Review 9 5. Data sources: Map of zones Shallow areas (above approximately 30 m deep) were mapped for this study using remote sensing imagery. The map of geographic zones was built using Landsat imagery and an object-oriented approach, and has a spatial resolution of 30 m. The map follows a zonation scheme adapted from Zitello et al. (2009) to capture the morphology of reef-rimmed platforms observed in the Miskitu cays and the non-rimmed, flat-topped platforms of the Eastern banks. The map of zones was used to identify (1) lagoon and back-reef areas; (2) fore-reef areas and (3) deep bank areas, relevant to recognize functional seascape units in the region. Although the map remains unvalidated due to logistical difficulties, broad geographic zones are generally identified using Landsat with reasonable accuracy (Andréfouët et al., 2006). Source imagery Available Landsat-8 imagery was assessed for cloud cover, suspended sediment load and the general degree to which the submerged habitats could be discerned. The best scenes (Table S5.I) were downloaded and mosaicked using ENVI image processing software. During construction of the mosaic, individual images were colour-balanced and feathered (a technique used to blend the suture lines between adjacent images in a mosaic by running a spatial filter over the seam) across the image boundaries over a distance of 500 m to smooth scene seams. Landsat channels 5-8 were used to mask out emergent areas prior to benthic image classification. Table S5.I. Landsat-8 imagery used as inputs to the classification Image ID# Date of Acquisition Path Row LC80140482014187LGN00 2014-07-06 14 48 LC80140492014187LGN00 2014-07-06 14 49 LC80140502014363LGN00 2014-12-29 14 50 LC80150482014354LGN00 2014-12-20 15 48 LC80150492014354LGN00 2014-12-20 15 49 LC80150482014354LGN00 2014-12-20 15 50 LC80160472014265LGN00 2014-09-22 16 47 LC80160482014265LGN00 2014-09-22 16 48 Methodology Geographic zones were delineated using an object-oriented approach. In contrast to pixel-based classification methods, object-oriented image analysis segments satellite data into landscape objects that have ecologically- meaningful shapes and classifies the objects across spatial, spectral and textural scales. Object-oriented methods have been shown to yield significant accuracy improvements over traditional pixel-based image analysis techniques (Kelly and Tuxen, 2009; Purkis and Klemas, 2011). Imagery was first radiometrically and atmospherically corrected using ENVI software to yield units of reflectance at the water surface. A water column correction was not applied in this study as the object-based strategy for mapping is not as confounded as a pixel-based classifier to bathymetric artefacts. This is because object-based mapping utilizes image texture, a property invariant to variable water depth (Purkis et al., 2006). Zones were classified using the software eCognition (v. 9.0, Trimble Inc.) and the multi-resolution segmentation algorithm with a scale parameter of 200. Zone boundaries within each platform were classified through visual identification of platform morphology. Areas were mapped according to a scheme adapted from Zitello et al. (2009, Figure S5.1) to capture the morphology of reefs in the region characterized by poor development. For the Miskitu Cays, the zone "reef flat" and “back-reef” was added to the Zitello’s atoll model to yield seven classes that were sufficient to capture the geographic zones of the platforms (Figure S5.1A). This model may be termed a “reef-rimmed” carbonate platform. Because the Eastern banks display even more depauperate reef development, further modification of the Zitello zones was required. The approach adopted here was to develop a zonation that was independent of the presence of coral reefs and instead keyed on platform morphology. The adapted scheme uses five zone classes (Figure S5.1B) and may be termed as a “flat-topped” carbonate platform. Equivalences between Zitello’s (2009) and the zonation schemes developed during the mapping of consolidated areas in eastern Honduras can be found in Table S5.II. Page 31 of 41 Privileged Communication For Peer Review 10 Figure S5.1. Map and zonation schemes developed for the “reef rimmed” morphology of the Miskitu cays (A) and the “flat-topped” morphology of the Eastern banks (B). Table S5.II. Equivalence matrix between Zitello et al. (2009) zonation scheme for an ‘atoll’ and the ‘reef-rimmed’ and ‘flat-topped’ geomorphology found within the study area. Atoll: Zonation scheme according to Zitello et al. Reef-rimmed: Zonation scheme used for the Miskitu cays Flat-topped: Zonation scheme used for the Eastern banks Lagoon Lagoon, Back-reef Platform top Reef crest Reef crest, Reef-flat Platform margin Fore-reef Fore-reef Platform slope Bank/Shelf/Escarpment Bank shelf/Escarpment Bank shelf/Escarpment Assessment The region encompasses a total area of shallow consolidated habitats of 24,947 km2 in Honduras, a 33-fold increase in coverage when related to previous global assessments of reef extent which only mapped 750 km2 of shallow habitats in this region (Andréfouët et al., 2006). The area can be divided into two geomorphologically distinct regions, the Miskitu cays and the Eastern banks, all atop the Nicaraguan rise. The Miskitu cays comprise a collection of 49 cays covering just 0.3 km2 of land and about 2,844 km2 of shallow consolidated habitats within Honduran waters. Shallow areas are distributed along ten reef-rimmed isolated carbonate platforms separated by deep structural lows (Figure S5.1A). The windward (eastern) margins of the platforms host well-developed reef rims, while leeward margins have less vigorous growth, languish in deeper waters and are fully exposed to marine conditions. The Honduran Eastern banks are large (22,103 km2 within Honduran waters), drowned structures atop the Nicaraguan rise (Figure S5.1B). With the exception of the windward margins of Gorda and Rosalinda banks, these flat-topped platforms have depauperated reefs and extensive shallow paved areas ideal habitat for lobster, conch and sea cucumber. Differences in geographic zonation among the Miskitu cays and the Eastern banks might be related to different development guided by different rates of flooding during the Holocene transgression, a mechanism that has been used to explain divergent morphologies of banks in the Bahamas (Purkis et al., 2014). Page 32 of 41Privileged Communication For Peer Review 11 6. Data sources: Larval connectivity matrix A larval connectivity matrix for spiny lobster was produced for this study. The dataset differs of similar ones available for the Caribbean basin (Kough et al., 2013) in spatial resolution and coverage: it represents a 18- fold increase in spatial resolution, and captures more than 24,000 km2 habitat areas in our study region that have been overlooked by global databases of reef extent (Andréfouët et al., 2006) and therefore in all previous efforts to assess larval connectivity patterns in the Caribbean. To model larval dispersal of spiny lobster in the Caribbean region, we developed a biophysical larval dispersal model using the individual-based offline Lagragian tool Ichthyop v3.1 (Lett et al., 2008). The virtual larvae were represented as particles in three dimensions and characterized by their latitude, longitude, and depth at each time step of the model (one hour). A forward-Euler advection was implemented in the model and horizontal diffusion was included following Peliz et al. (2007) with a turbulent dissipation rate of 10−9 m2s-3. Using coral reef habitat location from the Millenium Coral Reef Mapping Project (Andréfouët et al., 2006) and fishing grounds locations of lobster in Honduras, 4921 areas representing larval release and larval settlement locations were identified in the Caribbean region. Areas in Honduras were defined as 16 km2 square polygons whereas in the rest of the Caribbean release areas were 64 km2. Over these areas, 100,000 particles were randomly released from January 2006 to December 2008 in the HYCOM consortium global model (Chassignet et al. 2009). The HYCOM model fields for the intra America Seas region were extracted daily from the global model and converted to match Ichthyop’s input format. An ontogenetic vertical migration module was implemented to represent lobster larvae behaviour (Butler et al., 2011) following Callwood (2010). The larval dispersal duration was set to 196 days with 152 days of pre- competency period (Goldstein et al., 2008). Virtual larvae were considered settled when they were located in a settlement area and they were at least 152 days old. Simulations outputs are represented as connectivity matrices with dimensions 4,921x4,921, a vast improvement when related to 261 sites assessed by Kough et al. (2013). Patterns of larval connectivity in the Caribbean are extremely heterogeneous, with median larval dispersal distance ranging from 69 to more than 3,000 km (Figure S6.1). This Caribbean-wide connectivity matrix was subsetted to extract values for our study area. To this end, we assigned the closest connectivity value to each of our 1211 management units, and represented locations outside our region of interest as one unique additional site that represents the summation of all supplied and received larvae from elsewhere in the Caribbean. Figure S6.1. Median larval dispersal of spiny lobster in the Caribbean for the period 2006-2008, showing large differences in regional retention across the basin Page 33 of 41 Privileged Communication For Peer Review 12 7. Data sources: Adult connectivity matrix As a consequence of home ranges mobile species become vulnerable to fishing outside the management unit. To reflect this behaviour, we calculated an exposure matrix, which indicates the probability of occurrence of the species in nearby management units as a function of its home range and the configuration of the habitat. This information was then used to parameterize adult spillover and calculate effective fishing mortality within the spatially explicit population model. Lobster movement Random diffusion patterns are generally assumed when exploring the response of fish populations to protection from exploitation by marine reserves (e.g. Grüss et al., 2011; Moffitt et al., 2009). This is not realistic for many species that exhibit complex movement patterns (e.g. homing, migratory, nomadic) and restricted movement through habitat, such as spiny lobster, but also many fishes (e.g. Chapman and Kramer, 2000; Farmer and Ault, 2011). Panulirus argus participates in daily, seasonal, nomadic and ontogenetic movements (Butler et al., 2007; Herrnkind, 1980). Daily movements (also called homing) are short and random, where lobsters leave shelter to forage for food at night, encompassing about 1 km around dens (Bertelsen and Hornbeck, 2009). Seasonal migratory movements expand several kilometres and have been associated to reproductive activity, when lobster move from shallow inshore areas to deep reefs to spawn. Nomadic, undirected long movements are haphazard, individual and sporadic, and the causes are unclear. They occur with low probability of occurrence (of about 15%) over an area of about 4 km (Bertelsen, 2013). Finally, ontogenetic movements involve changes in habitats from back-reefs to patch-reefs and fore-reefs through the lobster’s life cycle. We considered all types of movement for the design of reserve networks for spiny lobster. Spawning and ontogenetic migrations occur within the seascape units. Daily homing and nomadic movements were modelled explicitly through the inclusion of an adult movement matrix, or exposure matrix, which we describe below. Exposure matrix The daily and nomadic movements of lobsters where characterized by an exposure matrix. Exposure E outside the management unit was calculated using the relationship given by Kramer and Chapman (1999, Eq. 1, Figure S7.1) where R is the ratio between the length of the management unit (5 km) and the home range.  = 100 1 −  <  < 0.5  = 100 IJKL <  > 0.5 Eq. 1 Following this equation, exposure equals 0.05 for daily movement (Ed) and 0.2 for nomadic movement (En). While daily movements occur all the time, nomadic movements are rare and occur only about 15% of the time. To calculate total exposure, we corrected exposure values by considering the probability of the specific type of movement to occur, and added them, given that the two forms of movement are independent (Eq. 2, Figure S7.1). This produced a total value of exposure of 0.08. ! = 1@ + 0.15& Eq. 2 Page 34 of 41Privileged Communication For Peer Review 13 Figure S7.1. Relationship between exposure and R (the ratio between reserve length and home range) according to Kramer and Chapman (1999) and calculation of E and corrected E (E’) for daily and nomadic movement. Lobsters generally remain within the habitat patch, with deeper, sand areas serving as habitat barriers (Acosta, 1999; Freeman et al., 2009), a phenomenon also common in some fishes (Chapman and Kramer, 2000; Farmer and Ault, 2011). This restricted behaviour implies that adult spillover will occur if cells in the Moore neighbourhood present continuous habitat. For simplicity, exposure in each of the Eij 8 neighbour cells was proportional to the amount of contiguous habitat available in the cell i (Eq. 3). :N = ! O87P∑O87QRPSTU Eq. 3 Using these constraints, an adult connectivity matrix Eij was calculated, reflecting the probability of an adult from area j to be present in area i. This information was used to calculate effective fishing mortality in each management unit within the spatially explicit population model. R=5/1= 5 Ed=0.05 R=5/4= 1.25 En=0.2 Movement type Home range (km) R E p E’ Daily 1 5 0.05 1 0.05 Nomadic 4 1.25 0.2 0.15 0.03 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 1 2 3 4 5 E x p o su r e Reserve length / Home Range Page 35 of 41 Privileged Communication For Peer Review 14 8. Data sources: Lobster parameters To estimate EPR and YPR we used the parameters described in Table S8.I. Because no population parameters for Honduran spiny lobsters have been compiled, we reviewed values reported for the Caribbean basin and chose typical ones, following, when available, the advice of research groups that have experience in stock assessment in the region: the Food and Agriculture Organization of the United Nations (FAO) and NOAA’s South-East Data, Assessment, and Review organization (SEDAR). The review for each parameter can be found below. The population model included 16 size classes. Individuals become reproductively mature at 2 years, at the same time they become available to the fishery. Fecundity increases with age. Individuals experience a natural mortality rate of 0.34 yr-1 throughout their lives and fishing mortality of 0.4 yr-1. Table S8.I. Parameters used for modelling EPR and YPR for Panulirus argus Parameter Value Definition Reference amax 16 Maximum age (year) Kanciruk 1980 tr 2 Age at recruitment (year) Munro 1983 tc 2.45 Age at first capture (year) Honduran legislation and morphometric relationship M 0.34 Instantaneous natural mortality rate FAO (2001), SEDAR (2010) F 0.4 Instantaneous fishing mortality rate SEDAR (2010) L∞ 183.55 Asymptotic von Bertalanffy length (mm) Leon et al. 2005 K 0.24 von Bertalanffy growth parameter Leon et al. 2005 t0 0.45 Age at which individual would be length 0 for von Bertalanffy (year) Leon et al. 2005 α 91.88 Parameter of fecundity-at-length relationship Cox and Bertelsen 1997 β 231212 Parameter of fecundity-at-length relationship Cox and Bertelsen 1997 b V1 < ≤ 32 < > 3 Number of broods per year SEDAR 2010 Γ 0.0046 Parameter of weight-at-length relationship Cruz et al. 1981 ∆ 2.630 Parameter of weight-at-length relationship Cruz et al. 1981 Maximum age (amax) We considered a maximum age of 16 years, which coincides with values used by SEDAR (2005, 2010) for population modelling of P. argus (Kanciruk, 1980). Age at recruitment (tr) We considered an age of 2 years, which corresponds to 60 mm, the recruitment size used by Munro (1983) for P. argus and Frisch and Hobbs (2012) for P. versicolor. Age at first capture (tc) In Honduras, regulations include a minimum legal size of 5.5 inches (140 mm) of tail length. This corresponds to approximately 70 mm of carapace length (CL) if an average of the morphometric functions considered in Table S8.II is used. As a reference, the minimum legal size for capture in the USA is 76.2 mm CL (SEDAR, 2010). This CL can, in turn, be transformed into age by considering the length-at-age relationship for spiny lobster, resulting in an age of first capture of 2.45 years. Table S8.II. Length (Lt) to carapace length (CL) relationships published for female lobsters Reference Location Equation CL for Lt=140 Ivo 1996* Brazil CL=0.5432Lt + 0.3442 76.39 Cruz et al. 1981* Cuba CL=0.3374Lt -2.3439 44.89 Zetina et al. 1996* Yucatan, Mexico CL=0.45Lt -0.06 62.94 Coba-Cetina 1990* Bahia de la Ascension, Mexico CL=0.56Lt -1.23 77.17 Gonzalez-Cano 1991* Quintana Roo, Mexico CL=0.5687Lt +0.01377 79.63 Wade et al. 1999 Belize CL=0.433Lt+17.37 77.99 Matthews et al. 2003 Florida CL=0.56*Lt-5.07 73.33 * References in FAO (2001) Page 36 of 41Privileged Communication For Peer Review 15 Instantaneous natural mortality rate (M) We used a constant value of natural mortality of 0.34 year-1 for all ages. This has been used recently by SEDAR (2010), and it falls within the range of 0.3-0.4 year-1 considered as most reliable for the Caribbean basin by FAO (2001) and SEDAR (2010). Values of natural mortality rate reported in the literature, however, range widely (Table S8.III), with a median of 0.36. Sources of variation could be related to differences in relative abundance of lobster predators in the area as well as the size structure of the particular populations (with smaller lobsters experiencing higher mortality). Table S8.III. Some natural mortality values reported in the literature for P. argus (both sexes). Reference M Location Ehrhard* 0.36 Bahamas Ivo 1996* 0.30 Brazil Gallo et al. 1998* 0.62 Colombia Buesa 1972* 0.26 Cuba Cruz et al. 1986a* 0.44 Cuba Cruz et al. 1981* 0.34 Cuba Powers and Sutherland 1989* 0.42 Florida, USA Muller et al. 1997* 0.30 Florida, USA Haughton 1988* 0.62 Jamaica Medley and Ninnes 1997* 0.36 Turks and Caicos * From SEDAR (2005) Instantaneous fishing mortality rate (F) Values reported for fishing mortality vary widely for the Caribbean among locations, years and methods, with minimums of 0.15 (SEDAR 2010) and maximum of 1.20 (FAO 2001). Although F is defined as the fraction of the average population abundance taken by fishing, and therefore one would expect it to take values less than 1, it can in practice have a value of more than 1 on an annual basis for stocks with a high biological regeneration rate such as lobster. In the USA, F values have been relatively constant around 0.21 during the last three years assessed. Here we considered values of 0.4. Length at age (L∞, K, t0) Because lobsters lack bony parts they cannot be aged in the same way as bony fish, in which annual increments in the ear-bones or otoliths are commonly used. Although recent efforts to age these crustaceans using other body structures have been underway (Maxwell et al. 2013), the lack of consistency in the relationship between age and length makes difficult to use these results to age lobsters using more novel methods (SEDAR 2010). Therefore length-at-age relationships for lobster are still derived from tag and recapture experiments, even though tagging is difficult for lobster due to their molting habits (SEDAR 2010). Although there are some criticisms to the use of von Bertalanffy-type functions for lobster because of the discontinuous growth of the species related to its molting habits (Ehrhardt 2008), the limited research on the subject and localized application (only Florida) precludes the consideration of discontinuous growth approaches at this time. FAO (2001) reviewed numerous parameter values for the application of the von Bertalanffy growth curve for female lobsters (Table S8.IV, Figure S4) and suggested the estimates of Leon et al. (1995) for Cuba as the most reliable, because of its large sample size. Since then, the same authors published updated parameter values, from 39 years of data (1963-2002) and 797,784 lobsters (Leon et al. 2005), and those were the values used here. According to Leon et al. (2005) K=0.24, L∞=183.55 and t0=0.45. Page 37 of 41 Privileged Communication For Peer Review 16 Table S8.IV. von Bertalanffy parameters for female P. argus. Parameters used highlighted in bold font Reference K L∞ t0 Location Waugh 1980* 0.23 190 0 Bahamas Evans 1988* 0.15 192 1 Bermuda Santos et al.1964* 0.38 148 0 Brazil Ivo 1996* 0.236 233 0 Brazil Gonzalez Cano and Rocha 1995* 0.18 162 0 Brazil Cruz et al. 1981* 0.31 139 0.08 Cuba SW Baez et al. 1991* 0.31 209 0 Cuba SW Phillips et al. 1992* 0.39 171 0 Cuba SW Leon et al. 1994* 0.24 174 0 Cuba SW Baez et al. 1994* 0.21 171 0 Cuba SW Leon et al. 1995* 0.19 155 0.37 Cuba Clairovin 1980* 0.23 188 0 Martinique Gonzalez-Cano 1991* 0.22 165 0.86 Mexico, Isla mujeres Gonzalez-Cano and Rocha 1995* 0.22 146 0 Mexico, Isla mujeres Arce 1990* 0.3 122 0 Mexico, Isla mujeres Lozano-Alvarez et al. 1991a* 0.25 215 0 Mexico, Bahia de la ascencion Castaño and Cadima 1993* 0.4 160 0 Nicaragua Olsen adn Koblic 1975* 0.32 133 0 Virgin Islands, USA Mateo & Tobias* 0.216 172.8 0.482 St. Croix Leon et al. 2005 0.24 183.55 0.45 Cuba SW *From FAO 2001, table 3.3 Fecundity at length (α, β) Different fecundity-at-length relationships have been published for P. argus which vary mainly in egg estimates for larger sizes (Table S8.V). Here we used the function by Cox and Bertelsen (1997), which is currently used by SEDAR (SEDAR 2010), and is an intermediate function within the ones that have been observed for the basin. According to Cox and Bertelsen (1997) lobsters reach maturity at 50.16 cm or 1.78 years if using the length-at-age relationship of Leon et al. (2005) discussed above. Table S8.V. Length-fecundity relationships published for P. argus. Also indicated the number of replicates and coefficient of determination (when present). Function used highlighted in bold font Reference Location N Equation Fonseca-Larios & Briones-Fourzan 1998 Puerto Morelos, Mexico 157 BS=3.40 CL2.5723 Nascimiento & Araujo 1984$ Rio Grande do Norde, Brazil 143 BS=9231.8519CL-477547.27, r2=0.97 Cruz et al. 1987$ Gulf of Batabano, Cuba 269 BS=0.5911 CL2.9866, r2=0.86 Cox and Bertelsen 1997 Dry Tortugas NP, USA - EC=91.88 CL2-231212 Cox et al. 1997° Florida Keys, USA 129 EC= 98.34 CL2 -1261651, r2=0.91 Cruz and Bertelsen 2008 Cuba, Florida Keys, Dry Tortugas and Mexico 658 EC=2.668CL2.709 Donahue et al. 1998° - - EC=88.7CL2-219200 $ Cited in Fonseca-Larios and Briones-Fourzan 1998, used by SEDAR (2005) ° Cited in FAO 2001 Broods per year (b) Large P. argus females produce several broods per year (Briones-Fourzán 2014, Cruz and Bertelsen 2008, Maxwell et al. 2009). Therefore, here we followed the approach used by Muller et al. (1997) and SEDAR (2010), and considered that female lobsters larger than 80 mm CL (i.e. 2.8 years using Leon et al. 2005 length-at-age equation) produce two broods per spawning season. Page 38 of 41Privileged Communication For Peer Review 17 Weight at length (Γ, ∆) Estimates of weight are needed to obtain yield. Many functions relating carapace length and tail weight have been published (Table S8.VI). With the exception of Mathews et al. (2003), Lyons et al. (1981) for males, and Wade et al. (1999) most functions are extremely similar. In this work we used the equation for both sexes published recommended by FAO (2001) in the absence of local data. Table S8.VI. Some mass at length relationships published for lobster. Function used highlighted in bold Reference Location N Equation Murray and Jennings-Clark 1998 St. Lucia 122 WTmale=0.030CL2.216, r2=0.85 St. Lucia 59 WTfemale=0.024CL2.270, r2=0.91 Lyons et al. 1981 Florida 312 WTmale=0.00315CL2.59934 Florida 258 WTfemale=0.00361CL2.68379 Florida 570 WTboth=0.0042CL2.64091 Cruz et al. 1981§ Cuba WTmale=0.00207 CL2.792 Cuba WTfemale=0.00279 CL2.736 Cuba WTboth=0.0046 CL2.630 Munro 1983 Jamaica 100 WTboth=0.00271 CL2.738 FAO 2001 Florida WTmale=0.00287 CL2.71 FAO 2001 Florida WTfemale=0.00195 CL2.81 SEDAR 2005 Puerto Rico WT=0.00921LC2.4804 Matthews et al. 2003 Florida WTboth=0.0007762 CL2.76273 Olsen and Koblic 1975* St. John WTboth=0.0021 CL2.778 Clairouin 1980* Martinique WTmale=0.0023 CL2.77 Clairouin 1980* Martinique WTfemale=0.0021 CL2.80 Squires and Riveros 1978* Colombia WTmale=0.00516 CL2.578 Squires and Riveros 1978* Colombia WTfemale=0.00221 CL2.7921 Wade et al. 1999* Belize Wboth=0.0012 CL2.689 § In FAO 2001 * In Matthews et al. 2003 Page 39 of 41 Privileged Communication For Peer Review 18 References Acosta, C.A. 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