Evaluating common indicators of the effects of marine protected areas on conservation and catches

Evaluating common indicators of the effects of marine 1 protected areas on conservation and catches 2 3 1 Introduction33 Various forms of spatial management have been used to conserve and manage marine ecosystems 34 across cultures throughout human history (e.g. Johannes 2002). The 1990s marked a period of 35 expanded interest in both the science and use of spatial management tools, specifically the general 36 concept of “marine protected areas” (MPAs) (Carr et al. 2019; Humphreys and Clark 2020). MPAs 37 are areas of the ocean where human activities are restricted or prohibited to promote biodiversity 38 conservation and potentially achieve other complementary objectives (Grorud-Colvert et al. 2021). 39 These objectives can include preserving cultural heritage, rebuilding populations inside protected 40 borders, providing conservation benefits outside in fished waters, and supporting surrounding 41 fisheries (Gaines et al. 2010). International movements such as the Montreal–Kunming Global 42 Biodiversity Framework’s call for protection of 30% of the oceans, and the Agreement under 43 the United Nations Convention on the Law of the Sea on the Conservation and Sustainable Use 44 of Marine Biological Diversity of Areas Beyond National Jurisdiction (the High Seas Treaty or 45 BBNJ) have provided substantial momentum for the expanded use of MPAs in the world’s oceans 46 in pursuit of these goals.47 Over 9% of the ocean is now covered by MPAs (as of October 2025; World Database of Protected 48 Areas), and the recent global expansion of MPAs has been matched by growing efforts to empir49 ically evaluate their performance (e.g. Osenberg et al. 2011; Edgar et al. 2014; Di Lorenzo et 50 al. 2020; Lynham and Villaseñor-Derbez 2024; Hopf et al. 2024) . Since many of the benefits 51 that MPAs are expected to deliver are difficult to measure directly, evaluations of MPA effects 52 often rely on tracking simpler indicators as proxies for broader MPA effects (Pelletier 2011; Hopf53 et al. 2024). These indicators enable assessments to be carried out across diverse contexts, and 54 have become a foundational tool for attempting to understand MPA effects in both scientific and 55 policy settings. Many indicators compare attributes within MPAs to nearby unprotected areas 56 (i.e., response ratios; Smith et al. (2024); Lester et al. (2009)), or from unprotected areas that are 57 near to MPA borders compared to those farther away (i.e., gradients, Halpern, Lester, and Kellner58 4 2009). More causally-robust approaches incorporate measurements both before and after MPA 59 implementation [i.e., before-after-control-impact or BACI; Medoff, Lynham, and Raynor (2022); 60 Lynham and Villaseñor-Derbez (2024); Kerr, Kritzer, and Cadrin (2019); Ovando et al. (2021)]. 61 While these empirical indicators differ in their complexity, each is presumably intended to deter62 mine the effect of the MPA on a particular observed metric: higher biomass in MPAs compared 63 to unprotected areas is interpreted as conservation gains within MPA borders (Smith et al. 2024; 64 Lester et al. 2009), while gradients in fisheries catch or effort are thought to signal evidence of 65 spillover of adult or larval fish from the MPA to surrounding waters (Halpern, Lester, and Kellner 66 2009; Medoff, Lynham, and Raynor 2022; Lynham and Villaseñor-Derbez 2024; Roberts et al. 67 2001). However, these indicator results are sometimes then assumed to also imply evidence for an 68 unobserved effect, such as changes in total population size or total fisheries catch. 69 The assumption that specific indicators can stand in for broader and harder to observe ecological 70 or social effects has not been to our knowledge comprehensively tested, despite their widespread 71 use (though works such as Hopf et al. (2024), Kerr, Kritzer, and Cadrin (2019), and Hilborn et al. 72 (2024) evaluated specific combinations of indicators and effects). Understanding the reliability of 73 indicators, and the variability of the underlying MPA effects they aim to measure, is critical for 74 interpreting existing evaluations, designing effective monitoring strategies, and for evidence-based 75 applied ecological decision-making. 76 This paper addresses two questions. We first analysed whether MPA effects on conservation 77 and catches are likely to be variable enough to justify the need for empirical monitoring. We 78 then tested the ability of several commonly used empirical indicators to reflect the actual effects 79 of MPAs. We found that MPAs can have highly variable effects on conservation and catches 80 depending on the specific social-ecological dynamics of the system in question, and that while 81 some indicators reliably track this variability in some MPA effects, many do not. 82 5 Materials and Methods83 MPA Experiment Overview84 We used a simulation framework to model both the variability of MPA effects and the performance 85 of empirical MPA indicators within complex social–ecological systems. We simulated a fishery 86 system with a set of bio-economic traits. We then ran an MPA experiment on that system by 87 generating two paired simulations identical in every way, except that one system contained a 88 no-take MPA and the other did not. We then calculated the simulated effects of the MPA on a 89 range of objectives based on the differences between the simulation with an MPA relative to 90 the paired simulation without an MPA. Lastly, we calculated common empirical indicators of 91 MPA performance from the simulation with the MPA, and compared these indicators to the true 92 simulated effects. We then repeated this process multiple times with different randomly generated 93 fishery states. The details of this process are explained below and illustrated in Figure 1.SeeSI 94 and Figure S1 for a case study simulation of these processes.95 Simulating Fisheries96 Fisheries systems were simulated using the marlin model (Ovando et al. 2023; Ovando 2025). 97 marlin simulates a user-specified number of age-structured fish populations fished by a user98 specified number of fleets on a simulated seascape divided into “patches” of defined area. For this 99 paper, we modeled a 21 by 21 grid of patches (441 total), each 25 km 2 (5 km × 5 km), for a total 100 seascape area of 11,025 km2.101 To explore MPA effects and indicators across a range of species, we modeled four species 102 archetypes defined by fixed and variable parameters, broadly based on a tuna (Thunnus albacares), 103 shark (Carcharhinus falciformis), grouper (Epinephelus fuscoguttatus), and reef fish (Seriola 104 quinqueradiata). Fixed parameters included growth, mortality, fecundity, recruitment, and move105 ment, with values based on the literature and our judgement (Table S1). We fixed these to avoid 106 6 Figure 1: Conceptual illustration of the process of simulating effects of MPAs, calculating empirical indicators, and comparing indicators to effects. Colored polygons in Step 2 indicate habitat distributions for each simulated species. See Methods section for detailed explanations of these steps. 7 unrealistic combinations of, for example, growth and mortality (Prince et al. 2015). Each iteration 107 of the model also used draws from a list of variable parameters (Table S2).108 The model simulates movement across the two-dimensional seascape through passive diffusion 109 and active taxis along habitat gradients, following J. T. Thorson et al. (2021) and Ovando (2025). 110 Movement rates of recruits and post-recruits were set so that 95% of individuals remained within 111 a given linear distance of their origin after one year. These distances were grouped into low (2.5 112 km), medium (25 km), or high (250 km) dispersal and assigned to recruit and post-recruit stages to 113 reflect a range of movement dynamics (e.g. sedentary adults and highly dispersed larvae, and vice 114 versa; Table S1). These values are not intended as true movement rates for the named species.115 For each simulation we augmented fixed parameters with random draws of variable parameters de116 scribing less-certain aspects of the system (Table S2). Ecological traits included the uniformity of 117 species-level habitat, the correlation in habitat across species, seasonal movement shifts, spawning 118 aggregations, the timing and strength of density dependence, and the magnitude and correlation 119 structure of recruitment deviation (Table S2). Variable traits also included fishery characteristics 120 such as fishing pressure on each species, speciesand fleet-specific economic value, the presence 121 of ports that affect spatial choices, and fleet selectivity (Table S2).122 Fish populations can be heterogeneously distributed in space, and species distributions can exhibit 123 positive, negative, or no correlations with other fished species (J. T. Thorson and Barnett 2017; 124 Karp et al. 2025; Brodie et al. 2021; Lopez et al. 2024). Following Ovando et al. (2023) and 125 Ovando (2025), for each species we randomly set a parameter 𝜅 describing habitat heterogeneity: 126 lower 𝜅 yields smoother habitat and higher 𝜅 yields more patchy habitat. We also generated a 127 habitat correlation matrix among species. These 𝜅 values and the correlation matrix were used to 128 construct a covariance matrix for a multivariate normal distribution, from which we drew spatial 129 habitat fields. These draws produce species distributions that vary across simulations in both their 130 heterogeneity and cross-species correlation.131 Our model also accounts for some of the complex behaviors of fishing fleets. Fleets can adapt 132 8 their spatial and temporal distribution in response to fishing opportunities and regulations. The 133 simulated effects of an MPA are sensitive to whether fishers adjust to new regulations, for example 134 by concentrating effort along MPA borders, which can strongly influence outcomes (Ovando 135 2025). 136 We allowed for different effort dynamics. For any given fleet in a simulation, total fishing effort 137 across patches was based on a random selection of either Constant Effort or Open Access. Under 138 Constant Effort, total effort is fixed over time unless a policy such as an MPA is implemented. Un139 der Open Access, total effort can expand or contract from year to year based on prior profitability 140 and under stable conditions evolves towards a bionomic equilibrium with zero profits (Costello et 141 al. 2016; Cabral et al. 2019). 142 Given total effort, fleets allocate effort across patches based on either profits or revenue, randomly 143 chosen for each fleet. When dynamics are profit-based, costs can increase with distance from the 144 fleet’s home port. MPA implementation can cause effort to redistribute or leave the fishery. Under 145 displacement, effort that was inside the MPA is reallocated to patches outside in the time step 146 following implementation, according to the fleet’s spatial rule. Under effort attrition, effort that 147 was inside the MPA exits the fishery. Under Open Access, total effort can subsequently adjust over 148 time. Together, these dynamics allow fleets to adjust both the total amount of effort and its spatial 149 distribution in response to opportunities and MPAs. 150 All else being equal, MPAs have greater effects in heavily fished systems than in lightly fished 151 ones (Hilborn et al. 2004). We simulated fishing pressure by randomly selecting a baseline fishing 152 mortality rate for each species, held constant in the absence of an MPA. Because the same fishing 153 mortality can have different effects depending on life history and selectivity, we summarize fishing 154 pressure using baseline “depletion”, measured as pre-MPA biomass (B) divided by unfished 155 biomass (B0), B/B0. Values near zero indicate heavily fished populations, and values near one 156 indicate lightly fished populations. The distribution of baseline B/B0 across simulations is shown 157 in Figure S25.158 9 The four species archetypes were used in three bio-economic fishery systems of increasing com159 plexity. The simple scenario is single-species, single-fleet, matching the most common way of 160 modeling MPA effects on one population and one fleet. The medium scenario is multi-species, 161 single-fleet, with all four species in the same seascape, allowing positively or negatively correlated 162 spatial distributions and variable vulnerability. The complex scenario is multi-species, multi-fleet, 163 with two fleets that differ in selectivity and fishing pressure, allowing dynamics such as a species 164 being targeted by one fleet and taken as bycatch by another.165 In total, each simulated fishery is built from combinations of fixed and variable bio-economic 166 parameters (Table S1; Table S2) and the chosen complexity level. We projected each fishery for 75 167 years to approximate pre-MPA equilibrium conditions.168 Simulating MPA Effects169 We ran each simulated fishery through an MPA experiment where all attributes of the simulated 170 fishery were held at identical values, except for the application of an MPA. Our MPA experiments 171 were created from a factorial combination of MPA size (represented as the percent of the surface 172 area of the seascape covered in a fully protected – i.e., no-take – MPA) and the placement strategy 173 of the MPA (Avoid Fishing or Target Fishing). MPA size ranged from 5% to 60% of the seascape, 174 in increments of 5%. Under the Target Fishing strategy, patches are placed in an MPA in descend175 ing order of total biomass caught, under the Avoid Fishing strategy, patches are placed in an MPA176 in ascending order of total biomass caught.177 We also explored how effects varied depending on whether the MPAs were individual entities 178 (contiguous) or divided across a network (mosaic) (Gaines et al. 2010; Pons et al. 2022). However, 179 all results presented here used the mosaic strategy since we tested the sensitivity of our results 180 to using contiguous MPAs and found no it had no meaningful impacts, so omitted those runs to 181 reduce computational overhead.182 After running each fishery for 75 years to reach equilibrium conditions, we then ran each fishery 183 10 through each MPA scenario for 20 more years. 20 years was selected to give enough time for MPA 184 effects to develop, without necessarily guaranteeing equilibrium conditions, reflecting the reality 185 of real-world MPA monitoring programs. Running the models for more years had no meaningful 186 effect on our results. After 20 years, we calculated the following MPA effects: 187 • Total biomass per species inside MPA borders (Biomass Inside)188 • Total biomass per species outside MPA borders (Biomass Outside)189 • Total biomass per species (Total Biomass)190 • Total catch per species and fleet (Catch)191 The true effects of the MPAs on each of these metrics was calculated by comparing the percentage 192 difference in the relevant values after 20 years post burn-in in the simulation with the MPA relative 193 to the paired simulation without the MPA. An MPA effect value of 20% means that the metric 194 in question was 20% higher in the simulation with the MPA than the same metric in the paired 195 simulation without the MPA. 196 Filtering Simulations 197 While we took steps to restrict the simulations to realistic scenarios (e.g. fixing core life history 198 traits), some combinations of parameters still produced implausible results, which were removed 199 from the final analysis. We removed simulations in which any species had extremely low baseline 200 depletion levels (less than 1% of unfished biomass), as while not impossible such extreme levels of 201 depletion are rare in marine fish populations and produce extreme results when considering MPA 202 effects on a percentage based scale. We removed any simulations in which any species had total 203 biomass values less than one, or any fishing fleet had catches less than one. These simulations 204 were removed since they resulted in improbably high percentage effect sizes. Post-filtering, the 205 combination of each simulated fishery with each MPA design resulted in a total of 10,896 unique 206 MPA experiments. 207 11 Total Biomass Catch Biomass Inside Biomass Outside 0-15% 15-30% 30-60% 0-15% 15-30% 30-60% -100% 0% 100% ≥200% -100% 0% 100% ≥200% -100% 0% 100% ≥200% -100% 0% 100% ≥200% Seascape in MPA MPA Effect B/B0 >50% 25-50% 0-25% Quantile 100% 80% 50% Figure 2: Distribution of simulation results across MPA effects (panels), proportion of seascape in MPA (columns), and level of baseline depletion in the absence of MPAs (colors, biomass B divided by unfished biomasss B0). Y-axis shows the “MPA effect”, the percent change in the outcome in question caused by the MPA. Biomass Inside refers to total individual species biomass inside MPA borders. Biomass Outside refers to total individual species biomass outside MPA borders. Total Biomass refers to total individual species biomass both inside and outside MPA borders. Catch refers to total catch per species and fleet outside the MPA. 18 Performance of Empirical Indicators of MPA Effects 315 The ability of empirical indicators to track MPA effects varied widely (Figure 3A). All three 316 inside-outside indicators had positive Spearman’s 𝜌 with Biomass Inside and Total Biomass,with 317 Biomass Density BACI having the highest 𝜌 values for both ( 𝜌 = 0.64 and 𝜌 = 0.45 respectively), 318 followed by Biomass Density Response Ratio ( 𝜌 = 0.56and 𝜌 = 0.38 respectively). All three 319 inside-outside indicators had negative Spearman’s 𝜌 values with Biomass Outside, meaning that 320 simulations with relatively higher biomass density response ratios were associated with simulations 321 with relatively lower Biomass Outside effects. 322 Gradient indicators exploiting near-far patterns around MPAs had much lower Spearman’s 𝜌323 values across all effects (all |𝜌| ≤ 0.2 ), explaining almost none of the rank-level variation in any 324 of the evaluated MPA effects. Among the near-far indicators, Effort Gradients had the highest 325 correlation values, (𝜌= 0.2 for Biomass Inside and 𝜌= 0.16 for Total Biomass) (Figure 3). 326 None of the evaluated indicators were meaningfully correlated with the effects of MPAs on total 327 catches, though all estimated correlations were negative. Biomass Density BACI had the clearest 328 negative correlation with MPA effects on catch, with 𝜌 = −0.14 (Figure 3). 329 The 𝜌 values shown in Figure 3indicate correlation between the indicator value and the outcome 330 value. These correlations tell us how reliably an indicator can be used to rank different MPAs in 331 terms of performance related to a specific MPA effect. We also examined how well raw indicator 332 values represented raw MPA effects by calculating measures of error (root mean squared error) and 333 bias (mean absolute error), where positive bias values indicate that, on average, indicator values 334 were higher than true values, and vice versa. These metrics are more useful for determining how 335 well the value of a given indicator at one MPA translates into the value of a given effects at the 336 same MPA. The average RMSE across all indicators was 93 percentage points, with an average 337 bias across all indicators of 13 percentage points. Most indicators were positively biased relative to 338 the true effect size, though some indicators were negatively biased for Biomass Inside and Total 339 Biomass.340 19 All of the results shown in Figure 3are based comparisons at the level of individual species and 341 where applicable fleets, for example comparing the Biomass Density BACI value for reef fish 342 to the true effect of the MPA on reef fish catches by an individual fleet. We also ran our results 343 on total values, comparing for example the Biomass Density BACI value aggregated across all 344 simulated species to the true effect of the MPA on all catches across all fleets (Figure S31). Doing 345 so had no substantial impact on the core results presented in the body of the paper.346 20 0.16 0.38 0.39 -0.02 0.45 0.06 0.2 0.56 0.54 -0.02 0.64 0.05 -0.03 -0.49 -0.4 -0.05 -0.47 0 -0.08 -0.07 -0.11 -0.02 -0.14 -0.09 Biomass Density Gradient Biomass Density Gradient BACI Effort Gradient Mean Length Response Ratio Biomass Density Response Ratio Biomass Density BACI A) Spearman’s ρ -1.0 -0.5 0.0 0.5 1.0 0.03 0.15 0.15 0 0.21 0 0.04 0.31 0.29 0 0.4 0 0 0.24 0.16 0 0.22 0 0.01 0.01 0.01 0 0.02 0.01 B) Spearman’s ρ² 0.00 0.25 0.50 0.75 1.00 109 90 55 69 86 65 118 77 88 100 69 96 116 128 42 58 125 53 143 144 77 87 143 84 Biomass Density Gradient Biomass Density Gradient BACI Effort Gradient Mean Length Response Ratio Biomass Density Response Ratio Biomass Density BACI Biomass Inside Biomass Outside Total Biomass Catch C) RMSE 050100 20 28 -26 -27 27 -28 -2 7 -48 -48 5 -49 48 57 2 2 56 1 68 76 23 22 75 21 Biomass Inside Biomass Outside Total Biomass Catch D) Bias -25 0 25 50 75 Figure 3: Spearman correlations 𝜌(A) and 𝜌2(B) between indicators (y-axis) and MPA effects (x-axis) at the level of individual species and fleets across all simulations. Root mean squared error (RMSE, C) and mean error (Bias, D) between indicators (y-axis) and effects (x-axis) at the level of individual species and fleets across all simulations. Plain text y-axis labels indicates inside-outside indicators, italic y-axis labels indicate a near-far indicator. Text shows the value of the metric in question, also reflected in the background color of each cell according to the associated colorbar legend. 21 California Response Ratio Case Study347 Sub-setting our results to only Biomass Density Response Ratio values that match the distribution 348 of response ratios for targeted species reported in Smith et al. (2024) allows us to visualize the 349 concepts shown in Figure 3. Simulated response ratios were positively correlated with Biomass 350 Inside and Total Biomass ( 𝜌 = 0.48 , 𝜌 = 0.37 ), and negatively correlated with Biomass Outside 351 and Catch (𝜌 = −0.28,𝜌 = −0.1) (Figure 4).352 While Biomass Density Response Ratios had a high 𝜌 value with Biomass Inside, there was sub353 stantial variation in this relationship, with low Biomass Density Response Ratios in fact being 354 associated with large changes in Biomass Inside, and vice versa. This was amplified for relation355 ships with lower correlations, such as Biomass Density Response Ratios and Catch, in which 356 Biomass Density Response Ratios of 0.5 could be produced by simulations with up to 100% in357 creases in catch or 100% losses in catch, or commonly with no meaningful change in catch at all 358 (Figure 4).359 22 ρ=0.48 ρ² = 0.23 ρ=0.37 ρ² = 0.14 ρ=-0.28 ρ² = 0.08 ρ=-0.1 ρ² = 0.01 Total Biomass Catch Biomass Inside Biomass Outside 0.0 0.5 1.0 0.0 0.5 1.0 -50% 0% 50% 100% 150% 200% 0% 100% 200% 300% 0% 100% 200% 300% 0% 50% 100% 150% 200% Simulated Biomass Density Response Ratio MPA Effect # of Simulations 25 50 75 100 125 Figure 4: Simulated Biomass Density Response Ratios (x-axis) plotted against simulated MPA effects (y-axis), with distribution of response ratios matched to empirical response ratios of targeted finfish reported by Smith et al. (2024). Constrained to MPA sizes besteen 10-40% of seascape and the scenarios with multiple co-existing species. Text shows Spearman 𝜌 correlations and 𝜌2values. 23 Discussion360 Our results show that MPA effects on conservation and catches can be highly variable in both 361 magnitude and direction, underscoring the need for monitoring and evaluating MPAs rather than 362 assuming their effects a priori.363 Variability of MPA Effects364 MPAs almost always increased Biomass Inside their borders (96% of simulations), though the 365 magnitude of these gains varied depending on variables such as MPA size, placement, and fishing 366 pressure. However, we also found that Biomass Outside the MPA declined in 52% of our simula367 tions, indicating that spillover from inside MPAs was often insufficient to overcome the effects 368 of concentrated fishing effort outside. Overall, increases in Biomass Inside MPAs were typically 369 large enough that Total Biomass (inside and outside) still increased in 88% of simulations, despite370 potential reductions in Biomass Outside.371 Our result that MPAs can reduce total biomass is perhaps unintuitive. Consider a scenario where 372 an MPA is placed on the core habitat of one species, but in doing so displaces fishing effort onto 373 the core habitat of another species. This displacement can result in a net increase in the total 374 fishing mortality on this second species, and a subsequent decline in total biomass. While these 375 negative effects on total biomass were relatively rare (12% of simulations), our findings highlight 376 the potential for unintended consequences of MPAs, particularly when fished species and fishing 377 fleets have heterogeneous distributions and behaviors Pons et al. (2022).378 While MPAs caused a net increase in Total Biomass in 88% of simulations, and a net increase in 379 Biomass Outside the MPA in 48% of simulations, MPAs reduced Catch in 73% of simulations. 380 This shows that in the majority of our simulations, MPAs caused a trade-off of better conservation 381 but lower catches. This trade-off was not due to a lack of spillover effects in our simulations, but 382 rather that in those simulations the amount of spillover from the MPA was not sufficient to make 383 up for the loss in fishing grounds caused by the protected area.384 24 However, our results also confirm that MPAs can produce win-win outcomes where biomass and 385 catch both increase (21% of simulations) more commonly when the fish population in question 386 would have been highly overfished in the absence of an MPA ( 35% of simulations where B/B0 387 ≤ 0.25), and the MPA size was not too large relative to the movement dynamics of the fished 388 species (or too small to have a meaningful effect) (Figure S29). Under these win-win conditions, 389 the spillover benefits of the MPA rebuilding an overfished population were sufficient to overcome 390 to loss in fishing grounds. 391 All else being equal MPAs had greater positive conservation effects in simulations with larger 392 MPAs and more overfished (lower B/B0) populations, and more negative catch effects in larger 393 MPAs and less heavily fished (higher B/B0) populations (Figure 2). However, these variables only 394 explained part of the distribution of MPA effects, with MPAs of the same size protecting equally 395 fished populations producing vastly different effects on conservation and catches depending on 396 other state variables ( Table S1; Table S2). Collectively, our results demonstrate that the effects 397 of MPAs on conservation and catches are a complex function of many interacting bio-economic 398 variables including MPA size, fish movement across different life stages, fishing pressure, and the 399 responses of fishing fleets to spatial closures. 400 Performance of MPA Indicators 401 Our findings complement past studies noting that common MPA indicators can perform well but 402 can also be misleading when faced the complex dynamics of marine social-ecological systems 403 (Hopf et al. 2024; Kerr, Kritzer, and Cadrin 2019; Hilborn et al. 2024; Claudet and Guidetti 2010; 404 Ferraro, Sanchirico, and Smith 2018; Christie et al. 2019). We extend this literature by providing a 405 comprehensive evaluation of the performance of multiple indicators as proxies for a range of MPA 406 effects under a wide set of bio-economic states. 407 The most reliable combination of indicators and effects were inside-outside indicators such as 408 Biomass Density BACI and Response Ratios as proxies for biomass effects of MPAs, with the 409 25 strongest correlations with Biomass Inside. Numerous studies have pointed out that inside-outside 410 indicators are likely to provide biased estimates of the conservation effects of MPAs given uncon411 trolled for violations to the core assumptions of these indicators such as differences in baseline 412 habitat inside versus outside, recruitment shocks, biological spillover, and fishing fleet responses, 413 are common in marine social-ecological systems (Ferraro, Sanchirico, and Smith 2018; Larsen, 414 Meng, and Kendall 2019; Hilborn et al. 2022; Ovando et al. 2021; Hopf et al. 2024). Our results 415 show that even when faced with these biasing factors, inside-outside indicators still could be rea416 sonably reliable proxies for the relative conservation performance of different MPAs, as evidenced 417 by the relatively high Spearman’s 𝜌 values (Figure 3). However, these inside-outside indicators 418 were still generally imprecise (high RMSE) and biased, indicating that one cannot reliably in419 terpret the specific values of an inside-outside indicator as the numerical effect on an MPA on 420 conservation.421 None of indicators evaluated in this study reliably tracked the effects of MPAs on fishery catches 422 (Figure 3). This highlights an urgent need for research on effective indicators of the effects of 423 MPAs on fishery catches, as our simulation results indicate that negative effects can be common. 424 Collection of actual data on the economic performance of fisheries (rather than indirect indicators 425 such as spillover gradients) could help provide better estimates of catch effects, though finding suit426 able “control” fisheries to isolate the causal effect of MPAs on total catch from other exogenous 427 shocks (e.g. changes in fuel prices or market demand) will be difficult.428 Near-far indicators exploiting gradients outside of MPAs methods have a long history in MPA 429 science (Halpern, Lester, and Kellner 2009; Lynham and Villaseñor-Derbez 2024; Medoff, Lyn430 ham, and Raynor 2022; Roberts et al. 2001; Di Lorenzo, Claudet, and Guidetti 2016; Methratta 431 2020). However, Near–far indicators failed to track any simulated MPA effect, despite our model 432 producing strong gradients in simulated biomass and effort (Figure S28). Both simulation model433 ing and empirical evidence have confirmed that some level of spillover will almost always occur 434 at one or more life stages given the movement dynamics of marine organisms (Cudney-Bueno 435 26 et al. 2009; Di Lorenzo et al. 2020; Franceschini, Lynham, and Madin 2024; Gaines et al. 2010; 436 Hilborn et al. 2004; Hilborn et al. 2024). The more relevant question is what does observing a 437 spillover gradient tell us? Our results show that under our simulated conditions, the presence of 438 true spillover gradients in for example biomass density or fishing effort caused by an MPA, is not 439 generally necessary nor sufficient evidence for the effects of MPAs on Biomass Inside,Biomass 440 Outside,Total Biomass, or Catch.441 Ensembles of near-far indicators might perform better than any individual one (Anderson et al. 442 2017). There are also other potential objectives of MPAs that may perhaps be reliably tracked 443 by gradient-based methods. For example, increases in the size and abundance of fish near MPA 444 borders may be of high value to recreational fishers (Franceschini, Lynham, and Madin 2024), 445 even if those increases on the border do not necessarily equate to commensurate benefits at the 446 scale of the total population or fishery. 447 The poor performance of near-far indicators as proxies for broader MPA effects in our model 448 presents a major challenge for evaluating MPAs where only fishery-dependent data from outside 449 MPAs are available. Evaluations of large high-seas MPAs created through efforts such as BBNJ 450 are likely to depend solely on fisheries data from outside the MPA (Medoff, Lynham, and Raynor 451 2022; Lynham and Villaseñor-Derbez 2024), as the costs to conduct fishery-independent surveys in 452 large and remote pelagic MPAs are likely to be prohibitive. Hampton et al. (2023) provides a good 453 example of integration of fishery-dependent data with process-based models to estimate the effects 454 of high-seas MPAs on tuna fisheries. Novel sources of data such as the acoustic signals collected 455 by Fish Aggregating Devices used in tuna fisheries could also be explored (Moreno et al. 2019). 456 It is important to note that even among the indicators with relatively higher correlations (inside457 outside), the sign of the correlation coefficient was not consistent. To illustrate, Biomass Density 458 Response Ratios observed in targeted fish species around California MPAs were generally pos459 itive, often substantially so (Smith et al. 2024). Our simulation results show that while higher 460 response ratios were generally produced by better Biomass Inside outcomes, higher Biomass 461 27 doi:10.1093/icesjms/fsz014.615 Larsen, Ashley E., Kyle Meng, and Bruce E. Kendall. 2019. “Causal Analysis in Control–impact 616 Ecological Studies with Observational Data.” Methods in Ecology and Evolution 10 (7): 617 924–34. doi:https://doi.org/10.1111/2041-210X.13190.618 Lester, S. E., B. S. Halpern, K. Grorud-Colvert, J. Lubchenco, B. I. Ruttenberg, S. D. Gaines, S. 619 Airamé, and R. R. Warner. 2009. “Biological Effects Within No-Take Marine Reserves: A 620 Global Synthesis.” Marine Ecology Progress Series 384: 3346.621 Lopez, Jon, Shane Griffiths, Bryan P. Wallace, Verónica Cáceres, Luz Helena Rodríguez, 622 Marino Abrego, Joanna Alfaro-Shigueto, et al. 2024. “Vulnerability of the Critically 623 Endangered Leatherback Turtle to Fisheries Bycatch in the Eastern Pacific Ocean. I. A 624 Machine-Learning Species Distribution Model.” Endangered Species Research 53 (March): 625 271–93. doi:10.3354/esr01288.626 Lorenzen, Kai. 2022. “Sizeand Age-Dependent Natural Mortality in Fish Populations: Biology, 627 Models, Implications, and a Generalized Length-Inverse Mortality Paradigm.” Fisheries 628 Research 255 (November): 106454. doi:10.1016/j.fishres.2022.106454.629 Lynham, John, and Juan Carlos Villaseñor-Derbez. 2024. “Evidence of Spillover Benefits from 630 Large-Scale Marine Protected Areas to Purse Seine Fisheries.” Science 386 (6727): 1276–81. 631 doi:10.1126/science.adn1146.632 Maunder, Mark N., Richard B. Deriso, Kurt M. Schaefer, Daniel W. Fuller, Alexandre M. Aires-da633 Silva, Carolina V. Minte-Vera, and Steven E. Campana. 2018. “The Growth Cessation Model: 634 A Growth Model for Species Showing a Near Cessation in Growth with Application to Bigeye 635 Tuna (Thunnus Obesus).” Marine Biology 165 (4): 76. doi:10.1007/s00227-018-3336-9.636 McElreath, Richard. 2020. Statistical Rethinking: A Bayesian Course with Examples in r and Stan. 637 2nd ed. CRC Texts in Statistical Science. Boca Raton: Taylor; Francis, CRC Press.638 Medoff, Sarah, John Lynham, and Jennifer Raynor. 2022. “Spillover Benefits from the World’s 639 Largest Fully Protected MPA.” Science 378 (6617): 313–16. doi:10.1126/science.abn0098.640 Methratta, Elizabeth T. 2020. “Monitoring Fisheries Resources at Offshore Wind 641 34 Farms: BACI Vs. BAG Designs.” ICES Journal of Marine Science 77 (3): 890–900. 642 doi:10.1093/icesjms/fsaa026.643 Moreno, Gala, Guillermo Boyra, Igor Sancristobal, David Itano, and Victor Restrepo. 2019. “To644 wards Acoustic Discrimination of Tropical Tuna Associated with Fish Aggregating Devices.” 645 PLoS ONE 14 (6): e0216353. doi:10.1371/journal.pone.0216353.646 Nickols, Kerry J., J. Wilson White, Dan Malone, Mark H. Carr, Richard M. Starr, Marissa L. 647 Baskett, Alan Hastings, and Louis W. Botsford. 2019. “Setting Ecological Expectations for 648 Adaptive Management of Marine Protected Areas.” Journal of Applied Ecology 56 (10): 649 2376–85. doi:https://doi.org/10.1111/1365-2664.13463.650 Osenberg, Craig W., Jeffrey S. Shima, Sonja L. Miller, and Adrian C. Stier. 2011. “ECOLOGY – 651 Assessing Effects of Marine Protected Areas: Confounding in Space and Possible Solutions.” 652 In, edited by Joachim Claudet, 143–67. Ecology, Biodiversity and Conservation. Cambridge: 653 Cambridge University Press. doi:10.1017/CBO9781139049382.010.654 Ovando, Daniel. 2025. “Predicted Effects of Marine Protected Areas on Conservation and Catches 655 Are Sensitive to Model Structure.” Theoretical Ecology 18 (1): 7. doi:10.1007/s12080-024656 00602-7.657 Ovando, Daniel, Darcy Bradley, Echelle Burns, Lennon Thomas, and James Thorson. 2023. “Sim658 ulating Benefits, Costs and Trade-Offs of Spatial Management in Marine Social-Ecological 659 Systems.” Fish and Fisheries 25 (2). doi:10.1111/faf.12804.660 Ovando, Daniel, Jennifer E. Caselle, Christopher Costello, Olivier Deschenes, Steven D. Gaines, 661 Ray Hilborn, and Owen Liu. 2021. “Assessing the Population-Level Conservation Effects of 662 Marine Protected Areas.” Conservation Biology 35 (6): 1861–70. doi:10.1111/cobi.13782.663 Ovando, Daniel, Dawn Dougherty, and Jono R. Wilson. 2016. “Market and Design Solutions to 664 the Short-Term Economic Impacts of Marine Reserves.” Fish and Fisheries 17 (4): 939–54. 665 doi:10.1111/faf.12153.666 Pelletier, Dominique. 2011. “INDICATORS – Constructing and Validating Indicators of the 667 Effectiveness of Marine Protected Areas.” In, edited by Joachim Claudet, 247–90. Cambridge: 668 35 Cambridge University Press. doi:10.1017/CBO9781139049382.014.669 Pons, Maite, Jordan T. Watson, Daniel Ovando, Sandra Andraka, Stephanie Brodie, Andrés 670 Domingo, Mark Fitchett, et al. 2022. “Trade-Offs Between Bycatch and Target Catches in 671 Static Versus Dynamic Fishery Closures.” Proceedings of the National Academy of Sciences 672 119 (4). doi:10.1073/pnas.2114508119.673 Prince, Jeremy, Adrian Hordyk, Sarah R. Valencia, Neil Loneragan, and Keith Sainsbury. 2015. 674 “Revisiting the Concept of Beverton–holt Life-History Invariants with the Aim of Inform675 ing Data-Poor Fisheries Assessment.” ICES Journal of Marine Science 72 (1): 194–203. 676 doi:10.1093/icesjms/fsu011.677 Punt, André E. 2019. “Spatial Stock Assessment Methods: A Viewpoint on Current Issues and 678 Assumptions.” Fisheries Research 213 (May): 132–43. doi:10.1016/j.fishres.2019.01.014.679 R Core Team. 2024. R: A Language and Environment for Statistical Computing. Vienna, Austria: 680 R Foundation for Statistical Computing. http://www.R-project.org/.681 Roberts, Callum M., James A. Bohnsack, Fiona Gell, Julie P. Hawkins, and Renata Goodridge. 682 2001. “Effects of Marine Reserves on Adjacent Fisheries.” Science 294 (5548): 1920–23. 683 doi:10.1126/science.294.5548.1920.684 Smith, Joshua G., Cori Lopazanski, Christopher M. Free, Julien Brun, Clarissa Anderson, Mark 685 H. Carr, Joachim Claudet, et al. 2024. “Conservation Benefits of a Large Marine Protected 686 Area Network That Spans Multiple Ecosystems.” Conservation Biology n/a (n/a): e14435. 687 doi:10.1111/cobi.14435.688 Thorson, James T. 2019. “Guidance for Decisions Using the Vector Autoregressive Spatio689 Temporal (VAST) Package in Stock, Ecosystem, Habitat and Climate Assessments.” Fisheries 690 Research 210 (February): 143–61. doi:10.1016/j.fishres.2018.10.013.691 Thorson, James T., Steven J. Barbeaux, Daniel R. Goethel, Kelly A. Kearney, Edward A. Laman, 692 Julie K. Nielsen, Matthew R. Siskey, Kevin Siwicke, and Grant G. Thompson. 2021. “Estimat693 ing Fine-Scale Movement Rates and Habitat Preferences Using Multiple Data Sources.” Fish 694 and Fisheries 22 (6): 1359–76. doi:10.1111/faf.12592.695 36 Thorson, James T., and Lewis A. K. Barnett. 2017. “Comparing Estimates of Abundance Trends 696 and Distribution Shifts Using Singleand Multispecies Models of Fishes and Biogenic Habi697 tat.” ICES Journal of Marine Science 74 (5): 1311–21. doi:10.1093/icesjms/fsw193.698 Thorson, James T., and Kasper Kristensen. 2024. Spatio-Temporal Models for Ecologists. First 699 edition. Chapman & Hall/CRC Applied Environmental Statistics. Boca Raton, FL: CRC Press, 700 Taylor & Francis Group. 701 Thorson, James, and Kasper Kristensen. 2024. Spatio-Temporal Models for Ecologists. New York: 702 Chapman; Hall/CRC. doi:10.1201/9781003410294.703 Tredennick, Andrew T., Giles Hooker, Stephen P. Ellner, and Peter B. Adler. 2021. “A Practical 704 Guide to Selecting Models for Exploration, Inference, and Prediction in Ecology.” Ecology 102 705 (6): e03336. doi:10.1002/ecy.3336.706 White, J. Wilson, Louis W. Botsford, Marissa L. Baskett, Lewis AK Barnett, R. Jeffrey Barr, and 707 Alan Hastings. 2011. “Linking Models with Monitoring Data for Assessing Performance 708 of No-Take Marine Reserves.” Frontiers in Ecology and the Environment 9 (7): 390–99. 709 doi:10.1890/100138.710 White, J. Wilson, Andrew Rassweiler, Jameal F. Samhouri, Adrian C. Stier, and Crow White. 711 2014. “Ecologists Should Not Use Statistical Significance Tests to Interpret Simulation Model 712 Results.” Oikos 123 (4): 385–88. doi:https://doi.org/10.1111/j.1600-0706.2013.01073.x.713 Zuur, Alain F., ed. 2009. Mixed effects models and extensions in ecology with R. Statistics for 714 biology and health. New York, NY: Springer. 715 37