Evaluating the Reliability of Common Indicators for Assessing Marine Protected Area Effects on Conservation and Catches

Evaluating common indicators for assessing marine 1 protected area effects on conservation and catches 2 Daniel Ovando 3 Cori Lopazanski 4 1 Title Page5 Manuscript title: Evaluating common indicators for assessing marine protected area effects on 6 conservation and catches7 Short Title: Evaluating common indicators of MPA effects8 Authors: Daniel Ovando1* & Cori Lopazanski2,3 9 1 Inter-American Tropical Tuna Commission, Ecosystem & Bycatch Group, 8901 La Jolla Shores 10 Drive, La Jolla, CA, 92102, USA11 2 Duke University Marine Laboratory,Nicholas School of the Environment Beaufort, NC, 28516, 12 USA13 3 University of California Santa Barbara, Bren School of Environmental Science & Management, 14 Santa Barbara, CA, 93106, USA15 *Corresponding author: [email protected]16 Open Research statement: No data were collected for this study. This submission uses novel code, 17 which is provided, per our requirements, in an external repository to be evaluated during the peer 18 review process. The link to this external repository is https://github.com/DanOvando/mpa-effects-19 and-indicators. A pre-print archive of the code along with all results needed to reproduce this paper 20 is also available at https://zenodo.org/records/17308921. This Zenodo repository will be upgraded 21 to a permanent archive of the final results and paper upon publication.22 Key Words: Marine Protected Areas, Conservation effectiveness, Bio-economic modeling, Pro23 tected area evaluation, Fisheries management24 2 Abstract853 Marine protected areas (MPAs) are spatial management tools designed to ideally benefit diverse 854 conservation and social objectives, including biodiversity, food security, and climate resilience. 855 Because these objectives are often difficult to measure directly, evaluations of MPAs typically rely 856 on simplified empirical indicators—such as biomass inside versus outside MPAs, or gradients in 857 biomass across boundaries—as proxies for broader MPA effects. Yet in complex social–ecological 858 systems, even well-measured indicators may fail to capture the true causal effects of MPAs.859 Using a large-scale simulation framework (> 10,000 scenarios), we explored variability in MPA 860 effects and assessed whether common indicators reliably tracked intended objectives of protected 861 areas. We show that similarly sized MPAs can produce vastly different outcomes for conservation 862 and fishery catches depending on factors such as fishing fleet dynamics and habitat heterogeneity 863 within and across species. The degree of correlation between common empirical indicators of MPA 864 performance and the true effects of an MPA also varied widely. Indicators such as biomass density 865 response ratios were positively correlated with the effect of MPAs on biomass inside their borders 866 (Spearman’s 𝜌 = 0.56), but slightly negatively correlated with the effect of MPAs on total fishery 867 catches ( 𝜌 = -0.07). Common indicators of spillover, such as gradients in biomass density near 868 MPAs relative to far from MPAs, had little correlation with any conservation or catch outcome 869 (absolute value of Spearman’s 𝜌all ≤0.2).870 The high variability in MPA effects generated by our simulations highlights the importance of 871 effective ecological and economic monitoring programs designed to track the effects of MPAs. 872 However, our results also show that many indicators currently measured in and around MPAs may 873 contain little information on macro-level effects such as total changes in fish populations or fishery 874 catches. The next generation of MPA research urgently needs interdisciplinary collaboration to 875 develop sufficiently practical and reliable methods for tracking the effects of MPAs. Doing so will 876 help ensure that the planned rapid and global expansion of MPAs has the best chance of delivering 877 positive and equitable outcomes for nature and people.878 46 Introduction 25 Various forms of spatial management have been used to conserve and manage marine ecosystems 26 across cultures throughout human history (e.g. Johannes 2002). The 1990s marked a period of 27 expanded interest in both the science and use of spatial management tools, specifically the general 28 concept of “marine protected areas” (MPAs) (Carr et al. 2019; Humphreys and Clark 2020). MPAs 29 are areas of the ocean where human activities are restricted or prohibited to promote biodiversity 30 conservation and potentially achieve other complementary objectives (Grorud-Colvert et al. 2021). 31 These objectives can include preserving cultural heritage, rebuilding populations inside protected 32 borders, providing conservation benefits outside in fished waters, and supporting surrounding 33 fisheries (Gaines et al. 2010). International movements such as the Montreal–Kunming Global 34 Biodiversity Framework’s call for protection of 30% of the oceans, and the Agreement under 35 the United Nations Convention on the Law of the Sea on the Conservation and Sustainable Use 36 of Marine Biological Diversity of Areas Beyond National Jurisdiction (the High Seas Treaty or 37 BBNJ) have provided substantial momentum for the expanded use of MPAs in the world’s oceans 38 in pursuit of these goals. 39 Over 9% of the ocean is now covered by MPAs (as of October 2025; World Database of Protected 40 Areas), and the recent global expansion of MPAs has been matched by growing efforts to empir41 ically evaluate their performance (e.g. Osenberg et al. 2011; Edgar et al. 2014; Di Lorenzo et 42 al. 2020; Lynham and Villaseñor-Derbez 2024; Hopf et al. 2024) . Since many of the benefits 43 that MPAs are expected to deliver are difficult to measure directly, evaluations of MPA effects 44 often rely on tracking simpler indicators as proxies for broader MPA effects (Pelletier 2011; Hopf 45 et al. 2024). These indicators enable assessments to be carried out across diverse contexts, and 46 have become a foundational tool for attempting to understand MPA effects in both scientific and 47 policy settings. Many indicators compare attributes within MPAs to nearby unprotected areas 48 [i.e., response ratios; Smith et al. (2024); Lester et al. (2009)], or from unprotected areas that are 49 near to MPA borders compared to those farther away (i.e., gradients, Halpern, Lester, and Kellner 50 3 2009). More causally-robust approaches incorporate measurements both before and after MPA 51 implementation [i.e., before-after-control-impact or BACI; Medoff, Lynham, and Raynor (2022); 52 Lynham and Villaseñor-Derbez (2024); Kerr, Kritzer, and Cadrin (2019); Ovando et al. (2021)].53 While these empirical indicators differ in their complexity, each is presumably intended to deter54 mine the effect of the MPA on a particular observed metric: higher biomass in MPAs compared 55 to unprotected areas is interpreted as conservation gains within MPA borders (Smith et al. 2024; 56 Lester et al. 2009), while gradients in fisheries catch or effort are thought to signal evidence of 57 spillover of adult or larval fish from the MPA to surrounding waters (Halpern, Lester, and Kellner 58 2009; Medoff, Lynham, and Raynor 2022; Lynham and Villaseñor-Derbez 2024; Roberts et al. 59 2001). However, these indicator results are sometimes then assumed to also imply evidence for an 60 unobserved effect, such as changes in total population size or total fisheries catch.61 The assumption that specific indicators can stand in for broader and harder to observe ecological 62 or social effects has not been to our knowledge comprehensively tested, despite their widespread 63 use (though works such as Hopf et al. (2024), Kerr, Kritzer, and Cadrin (2019), and Hilborn et al. 64 (2024) evaluated specific combinations of indicators and effects). Understanding the reliability of 65 indicators, and the variability of the underlying MPA effects they aim to measure, is critical for 66 interpreting existing evaluations, designing effective monitoring strategies, and making evidence67 informed policy decisions.68 As MPA usage expands around the world, establishing expectations around potential MPA effects 69 and our ability to accurately measure them is essential to tracking progress towards outcomes 70 achieved, not just area protected. To that end, this paper addresses two questions. We first anal71 ysed whether MPA effects on conservation and catches are likely to be variable enough to justify 72 the need for empirical monitoring. We then tested the ability of several commonly used empirical 73 indicators to reflect the actual effects of MPAs. We found that MPAs can have highly variable 74 effects on conservation and catches depending on the specific dynamics of the system in question, 75 and that while some indicators reliably track this variability in some MPA effects, many do not.76 4 Methods 77 MPA Experiment Overview 78 We used a simulation framework to model both the variability of MPA effects and the performance 79 of empirical MPA indicators. The general structure of this simulation experiment is as follows. 80 We created a fishery system with a set of bio-economic traits. We then ran an MPA experiment 81 on that system by generating two paired simulations identical in every way, except that one 82 system contained a no-take MPA and the other did not. We then calculated the simulated effects 83 of the MPA on a range of objectives based on the differences between the simulation with an 84 MPA relative to the paired simulation without an MPA. Lastly, we calculated common empirical 85 indicators of MPA performance from the simulation with the MPA, and compared these indicators 86 to the true simulated effects. We then repeated this process multiple times with different randomly 87 generated fishery states. The details of this process are explained below and illustrated in Figure 1. 88 Simulating Fisheries 89 Fisheries systems were simulated using the marlin model presented in Ovando et al. (2023) and 90 Ovando (2025). marlin simulates a user-specified number of age-structured fish populations fished 91 by a user-specified number of fishing fleets, all operating in a two-dimensional space. This spatial 92 domain represents the surface area of the seascape, broken up into a series of “patches”, each 93 with a defined spatial area. For this paper, we modeled a 21 x 21 grid of patches (for a total of 94 441 patches), where each patch had a surface area of 25KM 2 (5 km x 5km), for a total simulated 95 seascape area of 11,025 KM2.96 To explore MPA effects and indicators across a range of species, we modeled four different species 97 archetypes made from a set of fixed and variable parameters. These simulated species were broadly 98 based on a tuna (Thunnus albacares), shark (Carcharhinus falciformis), grouper (Epinephelus 99 fuscoguttatus), and reef fish (Seriola quinqueradiata).Fixed parameters included those relating to 100 5 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. 6 growth, mortality, fecundity, recruitment, and movement, with values for each species based on 101 available literature and our own judgement (Table 1). We fixed these parameters in order to not 102 create unrealistic combinations of for example growth and mortality (Prince et al. 2015). 103 One of the key features of this model is the ability to simulate fish movement across the two104 dimensional seascape through both passive diffusion and active taxis in response to habitat gra105 dients, in the manner of J. T. Thorson et al. (2021) (see Ovando (2025)). Empirical estimates of 106 movement rates in the same units as those used in our simulation model were not readily available. 107 As such, we fixed movement rates of recruits and post-recruit fish such that 95% of animals were 108 within a given linear distance of their point of origin after one year of diffusion and taxis. We 109 grouped these distances into low (2.5km), medium (25km), or high (250km) dispersal distances, 110 and assigned these dispersal distances to the recruit and post-recruit life stages of each of our simu111 lated species based on our best judgement and a desire to reflect a range of movement dynamics 112 (e.g. sedentary adults and highly dispersed larvae, and vice versa) (Table 1). 113 For each simulation we augmented these fixed parameters with random draws of variable parame114 ters that describe other less-certain aspects of the simulation. These include the ecological traits 115 such as the uniformity of species-level habitat across the simulated seascape, the correlation in 116 habitat across species, seasonal movement shifts, spawning aggregations, the timing of density 117 dependence, the degree of recruitment deviation, and the temporal and cross-species correlations 118 in recruitment deviates (Table 2). Variable traits also included fishery characteristics such as the 119 magnitude of fishing pressure on each species, the economic value of each species for each fleet, 120 the presence of fishing ports affecting spatial fishing choices, and the selectivity of each fishing 121 fleet for each fished species (Table 2). 122 While all traits can have an impact on simulated effects, spatial variables are particularly important 123 for MPA effects, so we explain them in more detail here. The simplest assumption one can make in 124 an MPA model is that all else being equal fish biomass and fishing pressure are constant in space 125 and time, baring a policy intervention. Under these circumstances, in the absence of an MPA, fish 126 7 biomass and fishing effort are always the same in each patch. Following MPA implementation 127 in such a system, any differences in biomass or fish catches in any patch must be due to the MPA 128 itself.129 In reality, fish populations can be heterogeneously distributed in space at any given time step, 130 and their species distributions can exhibit positive, negative, or no correlations with other fished 131 species in the region. These spatial dynamics of species distributions are so pronounced in marine 132 systems that an extensive literature of Species Distribution Models (SDMs) has developed to 133 describe and model them (J. T. Thorson and Barnett 2017; Karp et al. 2025; Brodie et al. 2021) 134 (Lopez et al. 2024). This means that an MPA placed on core habitat can have very different effects 135 from a equally sized MPA placed on marginal habitat. Similarly, given that not all species have 136 the same habitat distributions, an MPA placed on the core habitat of one species may be protecting 137 marginal habitat of another.138 Following methods described in Ovando et al. (2023) and Ovando (2025), for each species within 139 each simulation we randomly set a parameter 𝜅 that describes the intrinsic heterogeneity of their 140 habitat across the simulated seascape; lower values of 𝜅 result in a smoother habitat distribution, 141 higher values of 𝜅 result in a more patchy habitat distribution. At the same time, we randomly 142 generated a habitat correlation matrix between each of the species in that seascape in a given 143 simulation. Using the methods described in Ovando (2025) based on J. T. Thorson and Barnett 144 (2017), these 𝜅 values for each species, along with the correlation matrix among all species, 145 are used to construct a covariance matrix. which in turn is used to simulate habitat in space as 146 a function of a multivariate normal distribution. We used this multivariate normal distribution 147 to generate random draws of species distributions that can vary across simulations both in their 148 heterogeneity and in their correlation across species, with for example some simulations resulting 149 in reef fish and groupers having pathcy and highly positively correlated habitats, and in others 150 smooth and highly negatively correlated habitats.151 Along with habitat heterogeneity, our model accounts for some of the complex behaviors of fishing 152 8 extreme levels of depletion are rare in marine fish populations and produce extreme results when 245 considering MPA effects on a percentage based scale. Similarly, we removed any simulations 246 in which any species had total biomass values less than one, or any fishing fleet had catches less 247 than one. These simulations were removed since they resulted in improbably high percentage 248 effect sizes (e.g. increases in catches of of 900% when catches increased from 0.1 MT to 1 MT). 249 Post-filtering, the combination of each simulated fishery with each MPA design resulted in a total 250 of 10,896 unique MPA experiments. 251 Calculating Empirical Indicators 252 The prior steps of simulating a fishery system under a range of MPA experiments create a distri253 bution of causal effects of MPAs on the selected metrics. We compared these true effects with 254 estimates from common empirical indicators of MPA performance. To isolate the fundamental 255 performance of the indicator from questions around data quality and bias, all indicators were 256 calculated using the simulated data without any observation error. 257 We evaluated six empirical indicators commonly used to assess MPA performance; Biomass 258 Density Before-After-Control-Impact ( BACI), Biomass Density Response Ratio,Mean Length 259 Response Ratio,Effort Gradient,Biomass Density Gradient,Biomass Density Before-After Gradi260 ent (Table 3). These indicators vary in their underlying response variable (biomass density, mean 261 length, or fishing effort), their spatial design (inside-outside or nearfar), and whether they include 262 temporal comparisons (before-after vs. after-only). These indicators were selected to represent a 263 range of approaches described in the empirical MPA literature to infer conservation and fisheries 264 effects. A full description of each indicator and its stylized equation is provided in Table 3.265 All models were fit using a log-normal distribution, with the dependent variable measured at the 266 resolution of species, patch, and time step (and by fleet where applicable). Coefficients from these 267 models can be interpreted as multiplicative effects; effect sizes are reported as percentage changes 268 using the transformation 100 × (𝑒𝛽𝑀𝑃𝐴 − 1) . All indicators were calculated at the species level, 269 15 as results were robust to aggregating biomass or catch across species (Figure S30).270 Indicators based on inside-outside comparisons (e.g., Biomass Response Ratio, Biomass BACI, 271 Mean Length Response Ratio) require the selection of a comparable reference site outside the 272 MPA. In empirical studies, reference sites are often selected to match the habitat and environ273 mental characteristics within the MPA (Chapman and Kramer 1999; Claudet and Guidetti 2010; 274 Osenberg et al. 2011; Smith et al. 2024). We approximated this reference site selection approach 275 by controlling for unfished biomass per patch and weighting regressions by distance from the MPA 276 border. Specifically, we calculated the linear distance of each patch from the nearest MPA border 277 and weighted models such that the the model pays the most attention to patches deepest inside the278 MPA and those farthest outside the MPA.279 Gradient (near-far) indicators (e.g., Effort Gradient, Biomass Gradient, Biomass Before-After 280 Gradient) compare metrics outside of MPAs based on distance from MPA borders. Following the 281 general approach of Medoff, Lynham, and Raynor (2022) and Lynham and Villaseñor-Derbez 282 (2024), we calculated the linear distance from each patch from the MPA border, and assigned 283 patches in the lowest 20th percentile of distance as Near and those in the top 80th percentile as 284 Far.Aswithinside-outside style analyses, we also controlled for unfished biomass per species per 285 patch.286 All models were fit using linear models in R (R Core Team 2024). For each indicator, variables 287 were measured without error at the resolution of spatial patch pand time step t. The spatial reso288 lution of the system is 21 by 21 patches, meaning that any given time step has 441 patches. For 289 models fit to a single time step then (e.g. Biomass Density Response Ratio), the number of data 290 points used to fit the model were N = 441. For models fit to multiple time steps of before and after, 291 (e.g. Biomass Density BACI), the number of data points used to fit the model were N = 882.292 16 Table 3: General structure of tested indicators of MPA effects. Bolded 𝛽parameter in Equation column indicates parameter interpreted as the effect of the MPA. Brefers to biomass, Erefers to effort, ML refers to mean length. INSIDE refers to patches plocated inside MPA borders (whether before or after MPA implementation), OUTSIDE to patches outside. AFTER refers to time periods tafter MPA implementation, BEFORE is before MPA implementation. NEAR are patches p outside but near the border of an MPA (whether before or after MPA implementation), FAR is outside and farther from the border of an MPA. Note that all regressions also include covariates for unfished total biomass across all species in each patch p, and weighting by absolute distance from MPA border. However we omit these ancillary terms from the table for clarity. Any indicator lacking a time term tis measured in the final time-step of the simulation, 20 years following MPA implementation. Indicator Estimated Effect and Key Assumptions Example Use Equation Biomass Density Before-After -Control-Impact (inside-outside) Ratio of change in Bafter MPA implementation inside MPA relative to outside MPA. Assumes Parallel trends in Binside and outside MPA preand post-implementation. Hopf et al. (2024) 𝑙𝑜𝑔(𝐵𝑝,𝑡)∼𝛽 0+ 𝛽1𝐼𝑁𝑆𝐼𝐷𝐸𝑝+𝛽 2𝐴𝐹𝑇𝐸𝑅𝑡 +𝛽3 𝛽3 𝛽3𝐼𝑁𝑆𝐼𝐷𝐸𝑝× 𝐴𝐹𝑇𝐸𝑅𝑡 Biomass Density Response Ratio (inside-outside) Post-MPA Ratio of B inside MPA relative to outside MPA. Assumes no pre-existing differences in Bbetween inside and outside sites Smith et al. (2024) 𝑙𝑜𝑔(𝐵𝑝)∼ 𝛽0+𝛽 1 𝛽1 𝛽1𝐼𝑁𝑆𝐼𝐷𝐸𝑝 Mean Length Response Ratio (inside-outside) Post-MPA ratio of ML inside MPA relative to outside MPA. Assumes no pre-existing differences in ML between inside and outside patches. Halpern (2003) 𝑙𝑜𝑔(𝑀𝐿𝑝)∼ 𝛽0+𝛽 1 𝛽1 𝛽1𝐼𝑁𝑆𝐼𝐷𝐸𝑝 Effort Gradient (near-far) Post-MPA ratio of Enear MPA relative to far. Assumes no pre-existing differences in Ebetween near and far patches. Goni et al. (2008) 𝑙𝑜𝑔(𝐸𝑝)∼ 𝛽0+𝛽 1 𝛽1 𝛽1𝑁𝐸𝐴𝑅𝑝 17 Indicator Estimated Effect and Key Assumptions Example Use Equation Biomass Density Gradient (near-far) Post-MPA ratio of Bnear MPA relative to far from MPA. Assumes no pre-existing differences in Bbetween near and far patches. Halpern, Lester, and Kellner (2009) 𝑙𝑜𝑔(𝐵𝑝)∼ 𝛽0+𝛽 1 𝛽1 𝛽1𝑁𝐸𝐴𝑅𝑝 Biomass Density Before-After Gradient (near-far) Ratio of change in Bafter MPA implementation near to MPA relative to far from MPA. Assumes Parallel trends in Bdensity near and far from MPA preand post-implementation. Lynham and Villaseñor-Derbez (2024) 𝑙𝑜𝑔(𝐵𝑝,𝑡)∼𝛽 0+ 𝛽1𝑁𝐸𝐴𝑅𝑝+𝛽 2𝐴𝐹𝑇𝐸𝑅𝑡+ 𝛽3 𝛽3 𝛽3𝑁𝐸𝐴𝑅𝑝× 𝐴𝐹𝑇 𝐸𝑅𝑡 We do not report uncertainty of estimates, as our primary objective is to evaluate relative perfor293 mance across indicators rather than to make statistical inference. Given that this is a simulation294 based analysis with arbitrarily defined sample sizes, conventional statistical significance testing is295 not meaningful (White et al. 2014), so we do not evaluate indicators against statistical significance 296 thresholds (e.g., p < 0.05). Similarly, we do not account for statistical complexities such as spatio297 temporal clustering (J. T. Thorson and Kristensen 2024) or zero-inflation (Zuur 2009). Applied use 298 of empirical indicators would need to be tailored to the local context, following best practices in 299 modeling and causal inference based on observational data from social-ecological systems.300 California Response Ratio Case Study301 The 10896 MPA experiments simulated in this study were generated to reflect a range of possible 302 bio-economic states and MPA design strategies. However, as a result there is no guarantee that 303 the distribution of simulated MPA effects within this range is reflective of the values seen in the 304 real world. To partly address this challenge, we created a subset of our simulations selected to 305 match the estimated response ratios from a network of MPAs along the coast of California, USA, 306 reported in Smith et al. (2024). These response ratios are reported at the level of individual MPAs, 307 with separate ratios for the total biomass density of targeted and non-targeted fishes. In order to 308 18 match these empirical response ratios, we sampled 2500 of our MPA experiments with replacement 309 using a weighting scheme designed to produce a distribution of Biomass Density Response Ratios 310 that matched those reported in Smith et al. (2024) (see Figure S27 ). We restricted the candidate 311 simulations for this process to MPA sizes between 10% and 40%, and to multi-species levels of 312 complexity, to more closely reflect plausible scenarios for the California system. This allowed us 313 to examine what range simulated MPA effects could be associated with the distribution of Biomass 314 Density Response Ratios measured in the California MPAs studied in Smith et al. (2024). Note that 315 we do not claim these as being simulations of the California MPA system itself, but rather a set 316 of simulations constrained to match a distribution of Biomass Density Response Ratios seen in a 317 real-world system. 318 Comparing MPA Effects and Indicators 319 The prior steps provide simulated MPA effects and indicator values for each MPA experiment. 320 We then assessed the ability of each indicator to track each outcome using a range of metrics. 321 We measured the correlation between each indicator and each outcome using Spearman’s rank 322 correlations ( 𝜌 ), given the potential for highly different scales between the indicator and the effects 323 and the potential for non-linear relationships between the indicator and the effects. We converted 324 these ρ values into ρ 2 values that reflect the proportion of the rank-order variance in the outcome 325 that is explained by the indicator. These Spearman’s rank correlation values provide a general 326 sense of the extent to which a higher indicator value in one MPA experiment and a lower indicator 327 value in another MPA experiment corresponds to a relatively higher outcome value at the first 328 MPA experiment and a relatively lower outcome value at the second MPA experiment. 329 To assess how accurately each indicator reflected the true outcome, we calculated the root mean 330 squared error (RMSE) and the mean error (Bias) for each indicator-outcome pair. These metrics 331 are expressed in percentage points, not percent differences. For example, a Bias of -20 means 332 that the indicator underestimated the true outcome by an average of 20 percentage points (e.g., 333 19 estimating 30% when the true value is 50%), not that it was 20% lower. Similarly an RMSE of 20 334 percentage points indicates typical deviations of about +/- 20 percentage points, not that the error 335 was within 20% of the true outcome.336 Reproducing Results337 All code needed to fully reproduce the results and manuscript are publicly available at https: 338 //github.com/DanOvando/mpa-effects-and-indicators and https://zenodo.org/records/17308921.339 Results340 Variability of MPA Effects341 Our simulated fisheries varied in their behavior as a function of the fixed (Table 1) and variable 342 (Table 2) simulation parameters. The degree of resulting fishing pressure, and subsequent deple343 tion, is one of the most important determinants of MPA effects. The median depletion ( 𝐵/𝐵0 ) 344 value across all our included simulations was 0.38, mean value 0.41, ranging from a minimum of 345 0.01and a maximum of 1.29 (noting that values above 1 are possible given recruitment variation).346 Our simulated MPAs had a wide range of effects on species-level biomass and catch, with both 347 positive and negative causal effects possible for all measured effects (Figure 2). Increasing MPA 348 size generally expanded the range of possible effects. MPAs caused an increase in Biomass 349 Inside their borders in nearly all simulations (96%), though negative effects were also observed 350 in 4%. In contrast, Biomass Outside MPA borders increased in 48% of simulations, indicating a 351 roughly even likelihood of positive or negative effects on biomass beyond MPA borders across 352 our simulations. This asymmetry (consistent biomass gains inside and variable effects outside) 353 resulted in a net increase in Total Biomass in 88% of simulations and a net decrease in 12% of 354 simulations. Negative MPA effects for Biomass Inside and Total Biomass were more common 355 when the MPA placement strategy was to avoid fishing and when fishing effort was displaced 356 20 by the MPA, as these scenarios generally resulted in the concentration of fishing effort in prime 357 habitat. The possibility of the MPA causing net losses in biomass increased with the level of 358 fishing pressure (Figure 2). 359 MPAs resulted in a net increase in speciesand fleet-level Catch in 27% of simulations, and a 360 net decrease in Catch in 73% of simulations. Smaller effect sizes on Catch (absolute effect sizes 361 less than 25%) were much more common than larger effect sizes. Using the Avoid Fishing MPA 362 strategy resulted in slightly lower frequency of net catch losses than the Target Fishing strategy, 363 but only slightly less so. While negative catch effects still occurred across all simulated levels 364 of fishing pressure, the number of simulations with positive catch effects increased with the 365 counterfactual degree of fishing pressure (Figure 2). 366 21 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. 22 Performance of Empirical Indicators of MPA Effects 367 The ability of empirical indicators to track MPA effects varied widely (Figure 3A). All three 368 inside-outside indicators had positive Spearman’s 𝜌 with Biomass Inside and Total Biomass,with 369 Biomass Density BACI having the highest 𝜌 values for both ( 𝜌 = 0.64 and 𝜌 = 0.45 respectively), 370 followed by Biomass Density Response Ratio ( 𝜌 = 0.56and 𝜌 = 0.38 respectively). All three 371 inside-outside indicators had negative Spearman’s 𝜌 values with Biomass Outside, meaning that 372 simulations with relatively higher biomass density response ratios were associated with simulations 373 with relatively lower Biomass Outside effects. 374 Gradient indicators exploiting near-far patterns around MPAs had much lower Spearman’s 𝜌375 values across all effects (all |𝜌| ≤ 0.2 ), explaining almost none of the rank-level variation in any 376 of the evaluated MPA effects. Among the near-far indicators, Effort Gradients had the highest 377 correlation values, (𝜌= 0.2 for Biomass Inside and 𝜌= 0.16 for Total Biomass) (Figure 3). 378 None of the evaluated indicators were meaningfully correlated with the effects of MPAs on total 379 catches, though all estimated correlations were negative. Biomass Density BACI had the clearest 380 negative correlation with MPA effects on catch, with 𝜌 = −0.14 (Figure 3). 381 The 𝜌 values shown in Figure 3indicate correlation between the indicator value and the outcome 382 value. These correlations tell us how reliably an indicator can be used to rank different MPAs in 383 terms of performance related to a specific MPA effect. We also examined how well raw indicator 384 values represented raw MPA effects by calculating measures of error (root mean squared error) and 385 bias (mean absolute error), where positive bias values indicate that, on average, indicator values 386 were higher than true values, and vice versa. These metrics are more useful for determining how 387 well the value of a given indicator at one MPA translates into the value of a given effects at the 388 same MPA. The average RMSE across all indicators was 93 percentage points, with an average 389 bias across all indicators of 13 percentage points. Most indicators were positively biased relative to 390 the true effect size, though some indicators were negatively biased for Biomass Inside and Total 391 Biomass.392 23 All of the results shown in Figure 3are based comparisons at the level of individual species and 393 where applicable fleets, for example comparing the Biomass Density BACI value for reef fish 394 to the true effect of the MPA on reef fish catches by an individual fleet. We also ran our results 395 on total values, comparing for example the Biomass Density BACI value aggregated across all 396 simulated species to the true effect of the MPA on all catches across all fleets (Figure S31). Doing 397 so had no substantial impact on the core results presented in the body of the paper.398 24 cannot reliably interpret the specific values of an inside-outside indicator as the numerical effect on 488 an MPA on conservation). 489 None of indicators evaluated in this study reliably tracked the effects of MPAs on fishery catches, 490 demonstrated through low and negative Spearman’s 𝜌 values (all |𝜌| values < 0.15), high RMSE, 491 and generally positive bias (Figure 3). This highlights an urgent need for research on effective 492 indicators of the effects of MPAs on fishery catches, as our simulation results indicate that negative 493 effects can be common. Being able to reliably monitor catch effects will help communities identify 494 and adapt to negative catch effects as needed, and practitioners of all kind identify the circum495 stances in which MPAs benefited both conservation and catch so that lessons from those win-win 496 examples can be applied to other areas. Collection of actual data on the economic performance 497 of fisheries (rather than indirect indicators such as spillover gradients) could help provide better 498 estimates of catch effects, though finding suitable “control” fisheries to isolate the causal effect of 499 MPAs on total catch from other exogenous shocks (e.g. changes in fuel prices or market demand) 500 will be difficult. 501 Gradient-based near-far indicators, such as differences in biomass density or fishing effort near 502 relative to far from MPA borders, did not reliably track any of the effects evaluated here (Figure 3). 503 This does not mean that these gradients do not exist; our simulation model consistently produced 504 high gradient indicator values (Figure S28). Rather, our results show that the existence of strong 505 near-far gradients does not contain clear information on MPA effects at the population or fishery 506 level. 507 Both simulation modeling and empirical evidence have confirmed that some level of spillover will 508 almost always occur at one or more life stages given the movement dynamics of marine organisms 509 (Cudney-Bueno et al. 2009; Di Lorenzo et al. 2020; Franceschini, Lynham, and Madin 2024; 510 Gaines et al. 2010; Hilborn et al. 2004; Hilborn et al. 2024). The more challenging question 511 is what does observing a spillover gradient tell us? Our results show that under our simulated 512 conditions, the presence of true spillover gradients in for example biomass density or fishing effort 513 31 caused by an MPA, is not generally necessary nor sufficient evidence for the effects of MPAs on 514 Biomass Inside,Biomass Outside,Total Biomass, or Catch.515 Gradient-based methods have a long history in MPA science (Halpern, Lester, and Kellner 2009; 516 Lynham and Villaseñor-Derbez 2024; Medoff, Lynham, and Raynor 2022; Roberts et al. 2001; Di 517 Lorenzo, Claudet, and Guidetti 2016; Methratta 2020). These near-far approaches are appealing 518 in part because they can be calculated using only post-MPA fishery-dependent data, and do not 519 necessarily require establishing monitoring programs to track conditions pre-implementation or 520 survey within MPAs. While gradient methods were not effective indicators of any of the MPA 521 effects evaluated in this study, research is needed on whether there are modifications to these 522 designs that are effective for some use cases, given that fishery-dependent near-far data are often 523 all that are available and as such are likely to be used despite any associated warnings from works 524 such as this. For example, perhaps conditional on the life history of the species gradients at specific 525 distances are more meaningful than others.526 There are also many other potential objectives of MPAs besides those evaluated here, which may 527 perhaps be reliably tracked by gradient-based methods. For example, increases in the size and 528 abundance of fish near MPA borders may be of high value to recreational fishers (Franceschini, 529 Lynham, and Madin 2024), even if those increases on the border do not necessarily equate to 530 commensurate benefits at the scale of the total population or fishery. Research should also explore 531 whether ensembles of near-far indicators might perform better than any individual one (Anderson 532 et al. 2017).533 The poor performance of near-far indicators as proxies for broader MPA effects in our model 534 presents a major challenge for evaluating MPAs where only fishery-dependent data from out535 side MPAs are available. For example, evaluations of large high-seas MPAs created through 536 efforts such as BBNJ are likely to depend solely on fisheries data from outside the MPA (Medoff, 537 Lynham, and Raynor 2022; Lynham and Villaseñor-Derbez 2024), as the costs to conduct fishery538 independent surveys in large and remote pelagic MPAs are likely to be prohibitive. Hampton et 539 32 al. (2023) provides a good example of integration of fishery-dependent data with process-based 540 models to estimate the effects of high-seas MPAs on tuna fisheries. Novel sources of data such 541 as the acoustic signals collected by Fish Aggregating Devices used in tuna fisheries could also be 542 explored (Moreno et al. 2019). 543 It is important to note that even among the indicators with relatively higher correlations (inside544 outside), the sign of the correlation coefficient was not uniform. Inside-outside indicators were 545 positively correlated with Biomass Inside and Total Biomass, but negatively correlated with 546 Biomass Outside and Catch. This means that for example when comparing two MPAs, the MPA 547 with the higher Biomass Density Response Ratio may have the relatively better outcome for 548 Biomass Inside and Total Biomass, but the relatively worse outcome for Biomass Outside and 549 Catch. This highlights the importance of caution in interpreting the meaning of inside-outside 550 indicators, as our results suggest that higher inside-outside indicator values to not necessarily 551 imply better outcomes for all objectives. For example, Biomass Density Response Ratios observed 552 in targeted fish species around California MPAs were generally positive, often substantially so 553 (Smith et al. 2024). Our simulation results show that this distribution of response ratios could 554 be associated with net changes in catch ranging from effectively 0%, to as high as a near 50% 555 increase, or as low as a -50% decrease, with negative effects on catch more common at high 556 Biomass Density Response Ratios values (Figure 4). 557 Other studies have highlighted potential concerns with some common MPA indicators: Hopf et 558 al. (2024) and Kerr, Kritzer, and Cadrin (2019) demonstrated that while indicators such as BACI 559 designs and response ratios could track some conservation effects, they could also be misleading 560 under certain conditions. Hilborn et al. (2024) demonstrated that the presence of gradients in fish 561 biomass as a function of distance outside of an MPA were not necessarily reliable indicators of 562 effects on catch or catch rates. Claudet and Guidetti (2010) discussed qualitatively how failing 563 to account for factors such as degree of enforcement, social responses, and habitat heterogeneity 564 could reduce the reliability of MPA indicators. Our results confirm the conclusions of these studies, 565 33 and expand on them by providing a comprehensive evaluation of the performance of multiple 566 indicators as proxies for a range of MPA effects under a wide set of bio-economic states.567 We concur with Hopf et al. (2024) that while purely empirical methods have value, best-practice in 568 estimating the effect of MPAs should be to explicitly incorporate population and fleet dynamics 569 into estimation models, or baring that to place purely empirical results in the context of appropriate 570 theoretical predictions. Bayesian estimation techniques provide a natural means for encoding prior 571 information based on other studies or bio-economic theory. Use of spatio-temporal modeling to 572 appropriately standardize spatial observations (J. T. Thorson 2019) so that they can be passed to 573 or integrated into spatial stock assessments (Punt 2019) would be best practices for estimating 574 net changes in population and fishery effects associated with MPA implementation, though 575 these methods are highly dataand expertise-intensive. Rather than prescribing one solution, we 576 highlight here that there is an urgent need for finding methods that effectively measure effects 577 of interest of MPAs, particularly effects of MPA outside their borders, given the realities of data 578 constraints and the performance of indicators tested here.579 Caveats580 Our results depend on the assumptions embedded in the marlin operating model used here (Ovando 581 et al. 2023), which incorporates many common assumptions around population dynamics, move582 ment, and fleet dynamics. While alternate assumptions could be used, the core of our results are a 583 function of assumptions that are broadly representative of real fisheries: both fish and fishers move, 584 and there is often spatial and temporal heterogeneity in life history, movement, habitat use, and 585 fleet dynamics. While we have aimed to produce plausible simulated states (e.g. by constraining 586 the life history of the species to common archetypes), we cannot assign real-world likelihood 587 to any of our simulated states, and some states and their associated MPA effects and indicator 588 performances may be more typical in reality than others.589 The model also omits certain ecological processes, such as trophic interactions or temporal trends 590 34 in habitat or life history, which could yield different patterns and also further complicate empirical 591 evaluations of MPA effects. These temporal trends are likely to become increasingly important to 592 account for given the effects of climate change on global oceans (Fredston-Hermann et al. 2020). 593 Future work could test performance under system-specific dynamics and with more explicit 594 ecological linkages. We only assess a subset of possible MPA effects and their interactions. Other 595 harder to model effects could have important implications. For example, in scenarios where MPAs 596 decrease catch, the economic condition and food security of a community could still go up in total 597 if those decreases in catch were offset by the economic benefits of tourism opportunities caused by 598 an MPA (Ban et al. 2019). 599 In order to calculate our empirical indicators, we assumed that all data are observed without 600 error. This choice isolates indicator performance, but means that our results likely represent 601 optimistic estimates. Observation error and sample sizes will further affect how well indicators 602 track MPA effects. We also do not account for the possibility and effects of exogenous economic 603 shocks that might impact fishing activity. All simulated data were collected after 20 years of 604 MPA protection. MPA indicators and effects both evolve over time (Hopf et al. 2024; Ovando, 605 Dougherty, and Wilson 2016) and so future studies could further examine the ways in which 606 different time periods of sampling affect results. We assumed that MPAs are fully no-take and 607 were perfectly enforced; violations of either of these assumptions would further complicate 608 studies of MPA effects (Claudet and Guidetti 2010). Future work could consider the specific 609 magnitude of error and bias in estimated MPA effects resulting from different kinds and magnitude 610 of observation error. It is beyond the scope of this study to review best practices in causal inference 611 in spatial social-ecological systems, see Ferraro, Sanchirico, and Smith (2018), McElreath (2020), 612 Zuur (2009), Byrnes and Dee (2025), Punt (2019), J. Thorson and Kristensen (2024), Tredennick et 613 al. (2021), Grace (2024), White et al. (2011), Hopf et al. (2024), Hilborn et al. (2022), and Ovando 614 et al. (2021) for useful insights in this space. 615 35 Conclusions616 The coming decades are likely to see a rapid expansion in the use of MPAs of various forms, 617 both in coastal seas and in dynamic open-ocean systems. The simulation modeling informed by 618 bio-economic theory implemented here supports the basic conclusion that this expansion is likely 619 to produce conservation gains inside borders and at the total population level, though the exact 620 magnitude of these benefits is highly uncertain. However, the effects of these MPAs outside their 621 borders, on both biomass and catch, is far less certain and may be highly positive, highly negative, 622 or anywhere in between, with negative catch effects being more common in our simulations.623 As such, it is important that we be able to measure the effects of MPAs on a range of objectives, 624 so that we can quantify the costs and benefits produced by MPAs and subsequently adapt our 625 understanding of effective design and use of MPAs as needed. Our results show that while imper626 fect, some empirical indicators, particularly inside-outside indicators such as response ratios, can 627 be reliable indicators of conservation outcomes of MPAs, particularly inside their borders. But 628 that few empirical indicators commonly in use reliably track the effects of MPAs outside their 629 borders, particularly on fishery catches. Gradient based near-far methods (e.g. those that assess 630 spillover based on biomass densities near relative to far from MPA borders), while commonly used, 631 performed particularly poorly as an indicator of any MPA effect evaluated in this paper.632 The next generation of MPA research urgently needs collaboration across disciplines such as 633 conservation biology, ecology, fisheries, and social sciences to develop sufficiently reliable and 634 practical methods for tracking the effects of MPAs. Doing so will help ensure that future expansion 635 of protected areas in the world’s oceans stand the best chance of achieving positive and equitable 636 outcomes for nature and people.637 36 Acknowledgments 638 This paper was greatly aided by discussions with participants of the Area-Based Management 639 working group of the “Helping science advance policy in ocean conservation” workshop convened 640 by the The Center for Sustaining Seafood at the University of Washington, March 2-3 2024. 641 Author Contributions 642 DO and CL conceived of the study and wrote the manuscript. All analyses performed by DO. 643 Conflict of Interest Statement 644 The authors declare no conflicts of interest. 645 Data Availability Statement 646 Open Research statement: No data were collected for this study. This submission uses novel code, 647 which is provided, per our requirements, in an external repository to be evaluated during the peer 648 review process. The link to this external repository is https://github.com/DanOvando/mpa-effects649 and-indicators A pre-print archive of the code along with all results needed to reproduce this paper 650 is also available at https://zenodo.org/records/17308921. This zenodo repository will be upgraded 651 to a permanent archive of the final results and paper upon publication. 652 37 References653 Abbott, Joshua K., and Alan C. Haynie. 2012. “What Are We Protecting? Fisher Behavior and the 654 Unintended Consequences of Spatial Closures as a Fishery Management Tool.” Ecological 655 Applications 22 (3): 762–77. doi:10.1890/11-1319.1.656 Anderson, Sean C., Andrew B. Cooper, Olaf P. Jensen, Cóilín Minto, James T. Thorson, Jessica C. 657 Walsh, Jamie Afflerbach, et al. 2017. “Improving Estimates of Population Status and Trend 658 with Superensemble Models.” Fish and Fisheries 18 (4): 732–41. doi:10.1111/faf.12200.659 Ban, Natalie C., Georgina Grace Gurney, Nadine A. Marshall, Charlotte K. 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Garcia, Leah R. Gerber, Eric Gilman, 730 Quentin Hanich, et al. 2022. “Area-Based Management of Blue Water Fisheries: Current 731 Knowledge and Research Needs.” Fish and Fisheries 23 (2): 492–518. doi:10.1111/faf.12629. 732 40 The following graphs show the core life history functions resulting from the fixed parameters used 895 for each fish species template across all simulations, including the case study shown in Figure S1.896 48 shark tuna grouper reef_fish Longitude Latitude A) Biomass Distribution Without MPA alpha beta Longitude Latitude B) Effort Distribution 0.00 0.25 0.50 0.75 1.00 Time B/B0 C) B/B0 per species over time 0 25000 50000 75000 100000 alpha beta 0 25000 50000 75000 100000 Time Catch D) Catch per species per fleet over time With MPA Without MPA grouper reef_fish shark tuna Figure S1: Case study simulation. A) Distribution of biomass per species in space, with more darker colors indicating lower biomass. B) Distribution of fishing effort, with darker colors indicating lower fishing effort C) Evolution of depletion (biomass divided by unfished biomass) per species over time, with vertical line indicating year of 30% MPA implementation. D) Catch by species and fleet over time, with vertical line indicating year of 30% MPA implementation. For panels C and D, solid line indicates world with MPA, dashed line simulated counter-factual where MPAs are not implemented. 49 maturity_at_age ssb_at_age weight_at_age fec_at_age length_at_age m_at_age 051015 051015051015 1 2 3 4 0 10 20 30 40 25 50 75 100 0 10 20 30 40 0 10 20 30 40 0.00 0.25 0.50 0.75 1.00 age Value At Age Figure S2: Life history ogives for reef fish archetype 0e+00 1e+06 2e+06 3e+06 0.00 0.25 0.50 0.75 1.00 SSB/SSB0 Recruits Figure S3: Spawner-recruit function for reef fish archetype 50 Recruits:density dependence is pre_dispersal Post-Recruits -30 0 30 -30 0 30 -30 0 30 KM from center KM from center Density after one year 0.03 0.06 0.09 Figure S4: Diffusion rates for reef fish archetype at recruit and post-recruit life stages. Color shows the density of individuals in the seascape after being allowed to diffuse from one central patch over the course of one year. maturity_at_age ssb_at_age weight_at_age fec_at_age length_at_age m_at_age 051015 051015 051015 1 2 3 0 50 100 50 100 150 0 50 100 0 50 100 0.00 0.25 0.50 0.75 1.00 age Value At Age Figure S5: Life history ogives for tuna archetype 51 0e+00 1e+05 2e+05 3e+05 4e+05 0.00 0.25 0.50 0.75 1.00 SSB/SSB0 Recruits Figure S6: Spawner recruit function for tuna archetype Recruits:density dependence is pre_dispersal Post-Recruits -30 0 30 -30 0 30 -30 0 30 KM from center KM from center Density after one year 0.00223 0.00224 0.00225 0.00226 0.00227 Figure S7: Diffusion rates for tuna archetype at recruit and post-recruit life stages. Color shows the density of individuals in the seascape after being allowed to diffuse from one central patch over the course of one year. 52 maturity_at_age ssb_at_age weight_at_age fec_at_age length_at_age m_at_age 0510152025 0510152025 0510152025 0.2 0.4 0.6 0.8 0 25 50 75 100 125 50 100 150 200 0.0 2.5 5.0 7.5 10.0 12.5 0.0 2.5 5.0 7.5 10.0 12.5 0.00 0.25 0.50 0.75 1.00 age val_at_age Figure S8: Life history ogives for shark archetype 0 5000 10000 15000 0.00 0.25 0.50 0.75 1.00 SSB/SSB0 Recruits Figure S9: Spawner recruit function for shark archetype 53 Recruits:density dependence is post_dispersal Post-Recruits -30 0 30 -30 0 30 -30 0 30 KM from center KM from center Density after one year 0.25 0.50 0.75 Figure S10: Diffusion rates for shark archetype at recruit and post-recruit life stages. Color shows the density of individuals in the seascape after being allowed to diffuse from one central patch over the course of one year. maturity_at_age ssb_at_age weight_at_age fec_at_age length_at_age m_at_age 0102030 0102030 0102030 0.2 0.4 0.6 0.8 0 50 100 150 200 50 100 150 200 0 50 100 150 200 0 50 100 150 200 0.00 0.25 0.50 0.75 1.00 age val_at_age Figure S11: Life history ogives for grouper archetype 54 0 10000 20000 30000 40000 0.00 0.25 0.50 0.75 1.00 SSB/SSB0 Recruits Figure S12: Spawner recruit function for grouper archetype Recruits:density dependence is pre_dispersal Post-Recruits -30 0 30 -30 0 30 -30 0 30 KM from center KM from center Density after one year 0.25 0.50 0.75 Figure S13: Diffusion rates for grouper archetype at recruit and post-recruit life stages. Color shows the density of individuals in the seascape after being allowed to diffuse from one central patch over the course of one year. 55 Length 0510 15 Age 04080 120 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Alpha Length 0510 15 Age 04080 120 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Beta Figure S14: Selectivity ogives for reef fish in case study Length 0102030 Age 0100200 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Alpha Length 0102030 Age 0100200 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Beta Figure S15: Selectivity ogives for grouper in case study 56 Length 05101520 25 Age 0100200 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Alpha Length 05101520 25 Age 0100200 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Beta Figure S16: Selectivity ogives sharks in case study Length 0510 15 Age 0 50 100 150 200 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Alpha Length 0510 15 Age 0 50 100 150 200 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 measure selectivity Fleet Beta Figure S17: Selectivity ogives tunas in case study 57 alpha beta Before MPA After MPA Before MPA After MPA 0 1 2 3 4 5 0 2 4 6 Fishing Effort Near MPA Far from MPA Figure S24: Distribution and trends of effort per patch near versus far from MPA before-and-after MPA, for patches located outside the MPA. These are the simulated data that would be used to calculate a effort based before-after-control-impact gradient study. 64 Range of Simulated effects 897 The following graphs show results across the full range of simulations included in this study. 898 shark tuna grouper reef_fish 0.0 0.5 1.0 0.0 0.5 1.0 0 10 20 0 10 20 depletion count critter grouper reef_fish shark tuna Figure S25: Distribution of baseline simulated depletion values (B/B0) 65 Biomass Inside Biomass Outside Total Biomass Catch Biomass Density BACI Biomass Density Gradient BACI Biomass Density Gradient Biomass Density Response Ratio Effort Gradient Mean Length Response Ratio -1 0 1 2 -1 0 1 2-1 0 1 2-1 0 1 2 -1 0 1 2 -1 0 1 2 -1 0 1 2 -1 0 1 2 -1 0 1 2 -1 0 1 2 MPA Indicator VALUE MPA Effect # of Simulations 200040006000 Figure S26: Full distribution of every evaluated indicator (x-axis) and outcome (y-axis). Color shows the number of simulations in each bin. 66 Observed California Response Ratios Simulated Response Ratios -2 0 24 Biomass Density Response Ratio Figure S27: Distribution of observed biomass density response ratios from Smith et al. (2024) and distribution of simulated response ratios sampled to match observed biomass density response ratios. Biomass Density Response Ratio Effort Gradient Mean Length Response Ratio Biomass Density BACI Biomass Density Gradient BACI Biomass Density Gradient 0% 20% 40% 60% 0% 20% 40% 60% 0% 20% 40% 60% 0 0.5 0 0 0.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 ≥3.5 0 0.5 1 1.5 2 2.5 3 ≥3.5 0 0.5 1 1.5 2 2.5 3 ≥3.5 Seascape in MPA MPA Indicators Value Quantile 0.95 0.8 0.5 Figure S28: Distribution of simulated empirical indicators as a function of MPA size. 67 0-15% 15-30% 30-60% (0,0.25] (0.25,0.5] (0.5,0.75] (0.75,1.5] 0% 5% 10% 15% 20%0% 5% 10% 15% 20%0% 5% 10% 15% 20% catch:negligible & biomass:negative catch:positive & biomass:negative catch:negative & biomass:negative catch:positive & biomass:negligible catch:negligible & biomass:positive catch:positive & biomass:positive catch:negative & biomass:negligible catch:negligible & biomass:negligible catch:negative & biomass:positive catch:negligible & biomass:negative catch:positive & biomass:negative catch:negative & biomass:negative catch:positive & biomass:negligible catch:negligible & biomass:positive catch:positive & biomass:positive catch:negative & biomass:negligible catch:negligible & biomass:negligible catch:negative & biomass:positive catch:negligible & biomass:negative catch:positive & biomass:negative catch:negative & biomass:negative catch:positive & biomass:negligible catch:negligible & biomass:positive catch:positive & biomass:positive catch:negative & biomass:negligible catch:negligible & biomass:negligible catch:negative & biomass:positive catch:negligible & biomass:negative catch:positive & biomass:negative catch:negative & biomass:negative catch:positive & biomass:negligible catch:negligible & biomass:positive catch:positive & biomass:positive catch:negative & biomass:negligible catch:negligible & biomass:negligible catch:negative & biomass:positive Percent of Simulations Figure S29: Frequency of different outcome quadrants as a function percent of seascape in MPA (columns) and baseline B/B0 (rows). 68 Effects on Total Biomass and Catch Across All Fleets and Species 899 The core results of our paper are presented at the resolution of changes at the resolution of species 900 and/or fleet (e.g. reef fish by fleet alpha). Here we present our results aggregated across all species 901 and fleets within a simulation (e.g. change in total biomass across all species, or change in catch 902 across all fleets and species). 903 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 0-25% 25-50% >50% Quantile Range 100% 80% 50% Figure S30: Distribution of simulation results across effects (panels), proportion of seascape in MPA (columns), and level of baseline depletion (colors, biomass Bdivided 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 species biomass across all species outside MPA borders. Total Biomass refers to total species biomass both inside and outside MPA borders. Catch refers to total catch outside the MPA. 69 0.25 0.37 0.28 0 0.46 0.1 0.32 0.57 0.46 -0.06 0.73 0.08 -0.01 -0.3 -0.23 -0.03 -0.28 0.03 -0.15 -0.08 -0.09 0.01 -0.16 -0.1 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 0.06 0.14 0.08 0 0.21 0.01 0.1 0.33 0.21 0 0.53 0.01 0 0.09 0.05 0 0.08 0 0.02 0.01 0.01 0 0.03 0.01 B) Spearman’s ρ² 0.00 0.25 0.50 0.75 1.00 112 43 33 41 41 37 124 54 75 84 49 81 113 59 26 32 59 28 131 81 61 64 82 62 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 0 25 50 75 100 125 1 13 -10 -13 15 -13 -25 -13 -37 -39 -11 -39 15 27 3 1 28 0 23 35 11 8 36 8 Biomass Inside Biomass Outside Total Biomass Catch D) Bias -20 0 20 Figure S31: Spearman correlations 𝜌(A) and 𝜌2(B) between indicators (y-axis) and effects (x-axis) at the level of total change across all specices or 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. Blue plain text indicates inside-outside indicators, red italic axis labels indicates 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. 70 ρ=0.15 ρ² = 0.02 ρ=0.13 ρ² = 0.02 ρ=-0.27 ρ² = 0.08 ρ=0.02 ρ² = 0 Total Biomass Catch Biomass Inside Biomass Outside 0.0 0.4 0.8 0.0 0.4 0.8 -25% 0% 25% 50% 75% 0% 100% 0% 50% 100% 150% 200% 0% 20% 40% 60% 80% Simulated Biomass Density Response Ratio Simulated effect of MPA on.. # of Simulations 510152025 Figure S32: Simulated response ratios (x-axis) plotted against total simulated MPA effects (y-axis), for subset of scenarios more reflective of the California MPA network. Simulations selected such that distribution of simulated response ratios roughly matches distribution of empirical response ratios for targeted finfish in California MPAs, reported in Smith et al. (2024). 71