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Eukaryote composition (V9_PR2)Using V9_PR2 we were able to assign a total of 15 668 (shotgun) and 90 689 reads for the shotgun and amplicon data, respectively. These reads represented 14%, 54%, 0 and 32% (shotgun), and 0%, 29%, 0 and 71% (amplicon) unassigned cellular organisms, Bacteria, Archaea and Eukaryota, respectively. Within the eukaryotes, we determined 51 and 64 taxa for shotgun and amplicon data, respectively. Abundant taxa (average abundance >0.1% across all samples; 31 and 27 taxa in shotgun and amplicon, respectively) are shown in Fig. 2. The latter includes 23 taxa (including assignments made on “Eukaryota” level) that were shared between shotgun and amplicon, and four taxa only detected in the amplicon data (Fig. 2C).Fig. 2: Eukaryote composition in five Santa Barbara Basin sediment samples post-alignment with V9_PR2 database.Composition is shown in relative abundances for (A) shotgun, and (B) amplicon data (phylum-level). The surface sample should be considered with caution in both (A) and (B) due to the possibility of contamination (see “Methods”). C Venn diagram showing eukaryote taxa richness (phylum level) in the shotgun and amplicon data after alignment with the V9_PR2 database (diagram areas are proportional to the total number of taxa included, for a list of shared/non-shared taxa see Supplementary Material Fig. 1). Only taxa abundant on average >0.1% are included, as they make up >99% of the eukaryote composition.Full size imageWithin shotgun, the most abundant eukaryotes were Ascomycota (53%), Telonemia (11%), Eukaryota (not further determined, 8%), Polycystinea (4%), Dinophyceae (3.8%), Streptophyta (3.2%), Amoebozoa (3%), Cercozoa (1.6%), Bacillariophyta (1.6%), Arthropoda (1%). In the amplicon data, the most abundant eukaryotes were Ascomycota (33%), Apicomplexa (30%), Dinophyceae (9.5%), Stramenopiles (6.3%), Eukaryota (4.9%), Polycystinea (3.5%), Foraminifera (3.2%), Cercozoa (1.1%) and Chordata (1%). Thus, a total of 10 and 9 taxa were abundant with >1% (average across all samples) in the shotgun and amplicon data, including only five taxa (Ascomycota, Eukaryota, Dinophyceae, Polycystinea, Cercozoa) that were picked up by both methods (i.e., are amongst the shared taxa in Fig. 2C, Supplementary Material Fig. 1). Taxa detected by one method or the other were slightly rarer species (between 0.1 and 1% average relative abundance across all samples; Supplementary Material Table 3).The shotgun EBC detected two taxonomic groups, one prokaryotic (Gammaproteobacteria) and one eukaryotic (Poacea). The amplicon EBC detected 46 taxa, of which 12 were prokaryotes and 34 were eukaryotes, including dinoflagellate taxa (Dinophysis and Alexandrium), Calanoida and Bacillariophyta (copepods and diatoms, respectively; Supplementary Material Table 1). While any reads assigned to EBC taxa were removed from samples, including reads assigned to the Bacillariophyta node, reads assigned to Bacillariophyta at lower taxonomic levels (e.g., Bacillariophycidae, Bacillariaceae, etc.) remain summarised under the phylum-level Bacillariophyta node (Fig. 2).Relationship between Eukaryota composition and V9_PR2 reference sequence lengthV9_PR2 reference sequence-lengths for the relatively abundant taxa ( >0.1% across all samples, including all taxa that were shared and assigned below eukaryote-level, i.e., 22 taxa, see Supplementary Material Table 3) were around the overall average sequence length of the V9_PR2 database (121 bp) (Fig. 3). However, considerable length variation was observed, with most of the abundant taxa being represented by shorter than average reference sequences in the V9_PR2 database, and a few taxa (e.g., Arthropoda, Opisthokonta and Amoebozoa) with a number of reference sequences longer than average (Fig. 3).Fig. 3: Average sequence lengths for individual eukaryote taxa as per in the V9_PR2 database (A) and read counts for these taxa in shotgun (SG) and amplicon (Ampl) data (B).Listed are all taxa that occurred on average >0.1% across all samples in either the shotgun or amplicon dataset, or both. Only taxa that were determined in both shotgun and amplicon data are included.Full size imageWe determined a negative correlation between the average V9_PR2 reference sequence length (V9PR2AL) and the A:SG read counts ratio per taxon for all samples (rV9PR2AL,A:SG_1.2 = −0.27269, rV9PR2AL,A:SG_4.3 = −0.33233, rV9PR2AL,A:SG_7.3 = −0.28064, rV9PR2AL,A:SG_11.8 = −0.32559, rV9PR2AL,A:SG_16.4 = −0.30078). This means that shorter V9_PR2 reference sequences for our abundant taxa were associated with an overamplification of these taxa in the amplicon data (for average V9_PR2 reference sequence length of the abundant taxa and A:SG ratios see Supplementary Material Table 4).Eukaryota and Bacillariophyta sequence length and coverage post-V9_PR2 alignmentSequences assigned to Eukaryota in shotgun were on average 112 bp and in amplicon data 161 bp, i.e., shotgun reads were around ~50 bp shorter than amplicon reads (Table 2). Bases covered in shotgun were ~40 bp shorter than in amplicon data (Table 2). Similarly, sequences assigned to Bacillariophyta were on average 124 and 167 bp in shotgun and amplicon data, respectively, so showed an ~40 bp difference. For Eukaryota, there was a difference of ~23 bp and 29 bp between sequence length and coverage in shotgun and amplicon data, respectively. For Bacillariophyta, we found a ~36 and ~37 bp difference between sequence length and coverage in shotgun and amplicon data, respectively.Table 2 Lengths and coverage of sequences assigned to Eukaryota and Bacillariophyta in shotgun and amplicon data.Full size tableBacillariophyta read lengths and coverage were similar to those of Eukaryota, for both shotgun and amplicon data (Table 2). Variation in sequence lengths and coverage was much higher in shotgun than in amplicon data. We found no trend towards shorter (i.e., more fragmented) sequences with increasing subseafloor depth for either Eukaryota or Bacillariophyta in the shotgun data. Eukaryota shotgun read lengths were on average ~9 bp shorter (112 bp) than the average reference sequences in the V9_PR2 database (121 bp).Diatom composition detected via diat-rbcL and read length characteristicsA total of 60 (shotgun) and 80 674 (amplicon) reads were assigned to diatoms (Fig. 4). In total, 27 taxa were determined in the shotgun, and 140 in the amplicon dataset. When considering the “abundant” taxa (on average >0.1%), 27 and 49 diatoms were determined in the shotgun and amplicon data, respectively (Fig. 4). A total of 10 taxa were shared between the two datasets Bacillariophyta, Bacillariophycidae, Chaetoceros, C. cf. pseudobrevis 2 SEH-2013, Pseudo-nitzschia, P. fryxelliana, Thalassiosiraceae, Thalassiosirales, Thalassiosira and T. oceanica (Fig. 4C, Supplementary Material Fig. 2). Sequences assigned to diatoms via diat-rbcL were shorter (by ~16 bp) in the shotgun than in the amplicon data, with amplicon read lengths and coverage all 76 + 1 bases (Table 3).Fig. 4: Diatom composition in the Santa Barbara Basin sediment samples post-alignment with diat-rbcL database.Diatom composition is shown as relative abundance for (A) shotgun and (B) amplicon data. The surface sample should be considered with caution in both (A) and (B) due to the possibility of contamination (see “Methods”). C Venn diagram showing diatom taxa richness (species level) in the shotgun and amplicon data after alignment with the diat-rbcL database (diagram areas are proportional to the total number of taxa included, for a list of shared/non-shared taxa see Supplementary Material Fig. 2). Only taxa abundant on average >0.1% are included (in A, B, C).Full size imageTable 3 Bacillariophyta sequence lengths in shotgun and amplicon datasets.Full size tableNo diatoms were detected in the shotgun EBC, however, 45 taxa were determined in the amplicon EBC with most reads assigned to Chaetoceros spp. (especially, Chaetoceros debilis, C. socialis and C. radicans), several Thalassiosira and Pseudo-nitzschia species, as well as others (Supplementary Material Table 2).Comparison of V9_PR2 vs. diat-rbcL derived diatom compositionIn the shotgun data, 79 and 60 sequences were assigned to diatoms using V9_PR2 and diat-rbcL as the reference database, respectively, and composition differed considerably (Fig. 5). Using V9_PR2, diatoms were mostly assigned on relatively high taxonomic levels (e.g., Bacillariophyta) with few taxa being differentiated sporadically in the different samples (Fig. 5A, Supplementary Material Fig. 3). Using diat-rbcL, Chaetoceros, Thalassiosira and Pseudo-nitzschia were more prominent (Fig. 5B).Fig. 5: Comparison of diatom composition in Santa Barbara Basin sediment samples determined in shotgun and amplicon data using the V9_PR2 and diat-rbcL databases.Relative abundance of diatoms (genus level) in the shotgun data after aligning to (A) V9_PR2 and (B) diat-rbcL. Relative abundance of diatoms (genus level) in the amplicon data after aligning to (C) V9_PR2 and (D) diat-rbcL. The surface sample should be considered with caution in (A–D) due to the possibility of contamination (see “Methods”). Venn diagrams of shared and non-shared diatom taxa after alignment to the V9_PR2 (18S-V9) and diat-rbcL databases for the shotgun (E) and amplicon (F) data (species level, diagram areas are proportional to the total number of species included). For a complete species list and their read counts per sample see Supplementary Material Fig. 3, Supplementary Material Table 5.Full size imageIn the amplicon data, 329 sequences were assigned to diatoms using V9_PR2, and 80 674 using diat-rbcL. Using V9_PR2, few taxa were detected in the two top samples (Leptocylindrus and Fragilariaceae at 1.2 mbsf, Bacillariophycidae and Bacillariaceae at 4.3 mbsf) while the lowermost samples were more diverse (Fig. 5C). Using diat-rbcL, most reads were assigned to Thalassiosira, Chaetoceros, and Pseudo-nitzschia, with other taxa sporadically occurring at different depths (Fig. 5D). For a complete species list and their read counts see Supplementary Material Fig. 3, and Supplementary Material Table 5.We found large differences in the number of shared vs. non-shared taxa between shotgun and amplicon data, and V9_PR2 and diat-rbcL alignments (Fig. 5E, F). Database inspections showed that all taxa detected via V9_PR2 were also represented in the diat-rbcL database, except Rhizosoleniaceae. However, out of the 22 taxa exclusively detected via diat-rbcL in shotgun (Fig. 5E, F), 10 are only represented in the diat-rbcL database (Pseudo-nitzschia caciantha, P. dolorosa, Chaetoceros cf. contortus 1 SEH-2013, C. cf. lorenzianus 2 SEH-2013, C. cf. pseudobrevis 2 SEH-2013, Thalassiosirales, Thalassiosiraceae, Coscinodiscus wailesii, Arcocellulus mammifer, Meuniera membranacea, Supplementary Material Fig. 3). Similarly, out of the 134 taxa exclusively detected via diat-rbcl in amplicon, 84 were in this database only, noticeably including several species and strains of Chaetoceros, Pseudo-nitzschia, Thalassiosira and Cylindrotheca (eg., additions SHE-2013, BOF in species names), amongst others (see Supplementary Material Fig. 3, Supplementary Material Table 5). More

The Wuikinuxv, Kitasoo/Xai’xais, Heiltsuk and Nuxalk First Nations hold Indigenous rights to their territories, where all data were collected. Scientific staff who are members of these Nations or who work directly for them had direct approvals from Indigenous rights holders and were exempt from other research permit requirements. Collaborating DFO scientists worked in partnership with the First Nations to collect data in their territories..Sampling targeted rocky reefs, the preferred habitat for most Sebastidae38, which we located through local Indigenous knowledge or a bathymetric model49. Data were collected by four fishery-independent methods—shallow diver transects, mid-depth video transects, deep video transects, and hook-and-line sampling—detailed in earlier publications32,33,34,35,50,51 and summarized in Table 1. Data had a spatial resolution of ≤ 130 m2 and each sampling location (N = 2936 for Sebastidae, 2654 for sponges, 2321 for corals) was ascribed to a 1-km2 planning unit within the standardized grid used to design the MPA network (N = 632 for Sebastidae, 525 for sponges, 529 for corals, 516 inclusive of surveys for all taxonomic groups).Table 1 Survey methods used for data collection.Full size tableAlthough sampling encompassed 11 years (2006–2007, 2013–2021: Table 1), 84% of 1-km2 planning units were sampled during only one year (Appendix S2). Analyses, therefore, focus on spatial variability in species distributions and do not address temporal variability within planning units. When all years and methods are combined, 1-km2 planning units had a median of 3 samples (range = 1 to 80, Q1 = 2, Q3 = 6) (i.e., sum of dive transects, video sub-transects, and hook-and-line sessions). Supplementary Data Set 1 reports sampling effort by 1-km2 planning unit, survey type, and year (see Data Availability for link to these data).For each 1-km2 planning unit, u, we calculated hotspot indices for Sebastidae (BSEB,u), structural corals (BCor,u), and large-bodied sponges (BSp,u). These indices did not consider cup corals, whip-like corals or encrusting corals or sponges.As detailed below (Eqs. 1–4), each species of Sebastidae or genera of corals contributed to BSEB,u or BCor,u, according to their abundance weighted by Wt: a conservation prioritization score based on taxon characteristics. For the 26 species of Sebastidae that we observed, Wt equaled the sum of scores for (1) fishery vulnerability, using intrinsic population growth rate, r, as a proxy variable52,53, (2) depletion level, using the ratio of recent biomass to unfished biomass as a proxy variable, (3) ecological role, with trophic level as proxy, and (4) evolutionary distinctiveness14 (Table 2; Appendix S3). Because several rockfishes are very long-lived (i.e., have low values for r) and depleted, maximum potential scores were twice as large for fishery vulnerability and depletion level than for ecological role and evolutionary distinctiveness. Data for depletion level and evolutionary distinctiveness were unavailable for some species, and score calculations (detailed in Table 2) account for missing values (Appendix S3).Table 2 Criteria and equations used to calculate the conservation prioritization score, Wt, for each species of Sebastidae and for each taxa of structural corals.Full size tableFor the 6 genera of structural corals analyzed (Appendix S4), Wt depended on mean height (estimated from video transect images: Table 1), which correlates positively with vulnerability to physical damage from bottom-contact fishing gear (including longer time to recovery)20,54,55 and with strength of ecological role (e.g., amount of biogenic habitat and carbon sequestration increases with height)44,56 (Table 2, Appendix S4). Wt for corals did not include depletion level due to lack of data.The hotspot index for large-bodied sponges, BSp,u did not differentiate between species characteristics (i.e., ({W}_{t}=1)) and we pooled the abundances of all observed species of Hexactinellidae (Aphrocallistes vastus, Farrea occa, Heterochone calyx, Rhabdocalyptus dawsoni, Staurocalyptus dowlingi) and Demospongiae (Mycale cf loveni). This approach is consistent with regional fishery bodies worldwide, which treat large-bodied sponges as a single functional group57.To derive hotspot indices for each taxonomic group (Sebastidae, structural corals, or large-bodied sponges), we first developed a set of candidate generalized linear mixed models (GLMM) to explain relative abundance data for rockfish, corals, and sponges. For each GLMM, we estimated ({lambda }_{t,i,l}), the expected counts (or expected percent cover) for taxa t obtained with survey method i at point location l. (Point locations are individual dive transects, video transect bins, or hook-and-line timed sessions: Table 1.) Specifically,$${lambda }_{t,i,l}=gleft(beta {X}_{t,i,l}right)$$
(1)
$${C}_{t,i,l}mathrm {, or ,} {D}_{t,i,l}sim fleft({lambda }_{t,i,l}right)$$
(2)
where g was the link function for the GLMM and f the distribution for the likelihood function modelling either the observed counts C (negative binomial) for Sebastidae and structural corals or a combination of counts (negative binomial) and percent cover D (beta distribution) for large-bodied sponges. We used multiple GLMMs to model large-bodied sponges because deep video transects recorded actual counts whereas dive or mid-depth video transects recorded percent cover categories (Table 1).For each taxonomic group, we estimated a set of coefficients (beta) for the vector of X covariates that best estimated counts or percent cover. Our hypothesized covariates included the 1-km2 planning unit (modelled as a random intercept to control for repeated measures within a given planning unit), survey method, depth (including both linear or a 2nd order polynomial), and taxa. Each GLMM controlled for sample effort as an offset—effort was measured either as area covered by dive transects or video bins, or the duration of hook-and-line sessions. We also tested for possible covariate’s effects on the dispersion parameter (for the negative binomial GLMMs) and zero-inflation terms (for both the negative binomial and beta GLMMs). The best set of covariates to predict counts or percent cover were then chosen based on AIC model selection criteria. All models were fitted using ‘glmmTMB’58 in R version 4.0.259, and simulated residuals and diagnostic tests performed for each best-fit model using the package ‘DHARMa’60. For example, our best model for Sebastidae counts predicted 2% fewer zero counts than were observed.We applied depth and survey method selectivity criteria to reduce excessive zeroes in the count data that may be biologically unjustified (Appendix S5). For all taxon, if i detected t, then the method was valid for that taxon. If i did not detect t and t is a Sebastidae, then the method was valid (i.e., count = 0) only if the overall 10th and 90th percentiles of depths sampled by that method encompassed the expected depth range of t (Appendix S5). If i did not detect t and t is a coral or sponge (which are rarer than Sebastidae), then the method is valid only if the depth of the sampling event exceeded or equaled the minimum expected depth of t. Also, hook-and-line gear cannot systematically sample sessile benthic organisms or planktivores and this method was valid only for non-planktivorous Sebastidae (Appendix S5).Using the best-fit models from above, we calculated the expected count (or percent cover) per unit of effort, (mu), for taxa t observed with method i at each planning unit u:$${mu }_{t,i,u}=frac{{sum }_{l=1}^{{n}_{i,u}}left({lambda }_{t,i,l}right)}{{sum }_{l=1}^{{n}_{i,u}}left({mathrm{E}}_{t,i,l}right)}$$
(3)
where ({n}_{i,u}) was the total number of point locations sampled by that method within the planning unit and effort was either the cumulative area covered by dive or video surveys or the cumulative duration of hook-and-line sampling sessions within the planning unit. Because survey methods differed in their maximum values and potential biases (e.g., field of view is greater for divers than for video cameras; hook-and-line gear samples one fish at a time while visual methods can observe multiple fish simultaneously),({mu }_{t,i,u}) was rescaled as a min–max normalization,({mu }_{t,i,u}^{^{prime}}) (i.e., difference between the observed value and the minimum value across all u, divided by the range of values across all u).The hotspot index for each of Sebastidae, structural corals, and large-bodied sponges (denoted as taxonomic group g) was then calculated for each planning unit as:$${B}_{g,u }={sum }_{t=1}^{{n}_{s,g}}{sum }_{i=1}^{{n}_{m,g}}{mu }_{t,i,u}^{^{prime}}{W}_{t}$$
(4)
where Wt was the taxon-specific weighing factor (Table 2, Appendices S3, S4), ({n}_{s,g}) was the number of species in taxonomic group g, and ({n}_{m,g}) was the number of valid methods to sample group g.For each 1-km2 planning unit where all taxonomic groups were surveyed (N = 518), we then calculated the overall hotspot index:$${B}_{o,u }=H{sum }_{g=1}^{G}{B}_{g,u}.$$
(5)
where H is Shannon’s evenness index, with proportional abundance of each taxonomic group represented by BSEB,u, BCor,u, and BSp,u.Hotspot index values were normalized as the proportion of the maximum value and converted to decile ranks. Relationships between decile ranks and index values were nonlinear (Appendix S6).For Sebastidae, large-bodied sponges, and the overall hotspot index, we defined hotspots as planning units containing decile ranks 9 or 10: criterion which we deemed appropriate for the small spatial scales of conservation planning being used for the central portion of the Northern Shelf Bioregion (16-km2 planning units in Fig. 2). We are aware that other studies define hotspots based on a narrower range of values (e.g., top 10%26; top 2.5%28) but their context is generally one in which conservation planning is done at a much greater scale (e.g., ≈50,000-km2 grid cells26;1° latitude × 1° longitude grid cells28). For structural corals, which had near-zero index values in all but the top-ranking planning units (Appendix S6), we defined hotspots as planning units containing decile rank 10.Maximum depths sampled within planning units were deepest in the Mainland Fjord and shallowest in the Aristazabal Banks Upwelling Upper Ocean Subregion (Appendix S7). Accordingly, we used multiple logistic regression implemented with the ‘glm’ function in R to estimate the probabilities hotspot occurrence within 1-km2 planning units in relation to maximum depth sampled (including a 2nd-order polynomial) and Upper Ocean Subregion. Competing models were compared with AIC model selection procedures.Following the directive of Central Coast First Nations, decile rank distributions were mapped as 16-km2 planning units, u16 (N = 283 for Sebastidae, 264 for sponges, 263 for corals, 260 inclusive of surveys for all taxonomic groups), thereby protecting sensitive locations that would be revealed at smaller scales. To do so, we took the average between the maximum index value and the mean of the remainder of index values among the 1-km2 planning units, u, contained within each u16, and converted these values into decile ranks. This approach balances conservation prioritization among u16 that may have good average index values for multiple u, and u16 with a single high-ranking u among multiple low-scoring u. Relationships between decile ranks and hotspot index values also were nonlinear at this scale (Appendix S6). The same hotspot definitions developed for u apply to u16.Eighty one percent of 16-km2 planning units were sampled during only one or two years (Appendix S2). When all years and methods are combined, 16-km2 planning units had a median of 6 samples (range = 1 to 110, Q1 = 3, Q3 = 13). Supplementary Data Set 2 reports sampling effort by 16-km2 planning unit, survey type, and year (see Data Availability for link to these data). More

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Agent-resource affiliation networksWe consider games involving populations of agents that extract from multiple common-pool sources (which term we use for nodes representing resources in accord with previous related work15,16). Agents’ access to sources is defined by bipartite networks, wherein a link between an agent and a source indicates that the agent can access that source. This access is determined by some exogenous factors and remains fixed in time. The set of agents affiliated with a particular source (s) is denoted as ({mathbf{A}}_{s}), while the set of sources affiliated with a particular agent (a) is denoted as ({mathbf{S}}_{a}). The degree of an agent (a) is denoted by (m(a)), and the degree of a source (s) by (n(s)).To explore the effects of network topology upon extraction dynamics and wealth distributions, we generate ensembles of ({10}^{3}) networks, each having (50) agents and (50) sources and sharing mean agent degree (langle mrangle =5) and mean source degree (langle nrangle =5). All networks thus share the same total numbers of agents, sources, and links, but differ in how these links are distributed among agents and sources. We generate 9 network ensembles, each generated to represent a particular combination of one of three types of degree heterogeneity in its source degree distribution (U: uniform-degree, L: low-heterogeneity, or H: high-heterogeneity) with one of three similar distributions of agent degree (u, l, or h39) (Supplementary Information S1.1). Degree histograms, averaged over each ensemble, provide a representative source degree distribution ({P}_{mathbf{S}}(n)) and agent degree distribution ({P}_{mathbf{A}}(m)) for each network type (Fig. 2a and b). It is worth noting that the results of the simulations depend primarily on the degree distributions of agents and sources rather than on the overall size of the networks used (Supplementary Information S3.1).Figure 2(a) Source degree distributions and (b) Agent degree distributions for 9 network ensembles, each representing a combination of a Uniform-degree (U), Low-heterogeneity (L), or High-heterogeneity (H) source degree distribution with a uniform-degree (u), low-heterogeneity (l), or high-heterogeneity (h) agent degree distribution. Ensemble mean time-averaged quantities from pure free adaptation dynamics: (c) Agent payoffs (f(a)) as a function of agent degree (m(a)); (d) Collective extraction (overrightarrow{q}(s)) as a function of source degree (n(s)); (e) Source quality (b(s)) as a function of source degree (n(s)); and (f) Period of oscillation (T(s)) as a function of source degree (n(s)). Means are computed from simulations on ({10}^{3}) networks of each type.Full size imageNetworked CPR extraction gameOn these networks, we simulate iterative games in which agents vary the extraction effort that they apply to their affiliated sources, altering the quality of these sources; in turn, these changes in source quality then influence how agents adapt their extraction levels in subsequent rounds. The extraction effort exerted by agent (a) upon its affiliated source (s) is denoted as (q(a,s)). The total effort exerted by an agent (a), its individual extraction, is denoted by (overleftarrow{q}left(aright)=sum_{sin {mathbf{S}}_{a}}q(a,s)). The total effort exerted upon source (s), or its collective extraction, is denoted by (overrightarrow{q}left(sright)=sum_{ain {mathbf{A}}_{s}}q(a,s)). The quality of a source (s) is quantified by the benefit (b(s)) per unit extraction effort applied that the source provides. The cost associated with extraction is given by a convex (quadratic) function of (overleftarrow{q}left(aright)), such that marginal costs increase with individual extraction15,16. In addition to modelling the increasing costs (i.e., diminishing returns) associated with the physical act of extraction itself, this could also reflect escalating, informal social penalties that result from increasing extraction (i.e., “graduated sanctions”1,40). The net payoff accumulated by an agent (a) in a game iteration is thus$$fleft( a right) = left[ {mathop sum limits_{{s in {mathbf{S}}_{a} }} qleft( {a,s} right) cdot bleft( s right)} right] – frac{gamma }{2}{ }mathop{q}limits^{leftarrow} left( a right)^{2} ,$$
(1)

where (gamma) is a positive cost parameter.Bistable model of CPR depletion and remediationSources are bistable, meaning that at any time they can occupy one of two states: (1) a viable state, during which the source provides a benefit of magnitude (alpha) in return for each unit of extraction effort, and (2) a depleted state, during which this benefit is reduced by (beta) ((0 vec{q}_{{text{D}}} left( s right)} \ {0, } & {{text{if }} chi_{t – 1} left( s right) = 1{text{ and }}vec{q}_{t} left( s right) le vec{q}_{R} left( s right)} \ {chi_{t – 1} left( s right),} & {text{otherwise }} \ end{array} } right.$$
(3)
In the results that follow, we focus upon a uniform capacity scenario, wherein all sources share identical threshold values (vec{q}_{{text{D}}} left( s right) equiv vec{q}_{{text{D}}}) and (vec{q}_{{text{R}}} left( s right) equiv vec{q}_{{text{R}}} left( s right)). An alternative degree-proportional capacity scenario, in which threshold values increase with source degree, is discussed in the Supplementary Information (S3.4.2).Free adaptationUnder the free adaptation strategy, an agent updates its extraction levels independently at each of its affiliated sources depending on the state of each (Fig. 1b). As in the replicator rule often applied in networked evolutionary game models17,41,42, the rate at which an agent adapts its extraction levels within a time interval ({Delta }t) is proportional to the marginal payoff that the agent expects to attain thereby:$$frac{{{Delta }qleft( {a,s} right)}}{{{Delta }t}} = kfrac{partial fleft( a right)}{{partial qleft( {a,s} right)}},$$
(4)
where (k) is a rate constant. So, each extraction level (qleft( {a,s} right)) is updated according to$$q_{t + 1} left( {a,s} right) = q_{t} left( {a,s} right) + kleft[ {alpha – beta chi_{t} left( s right) – gamma {mathop{q}limits^{leftarrow}}_{t} left( a right)} right].$$
(5)
The higher an agent’s individual extraction (overleftarrow{q}(a)), the more slowly it will increase its extraction from viable sources, and the more rapidly it will reduce its extraction from depleted sources.Uniform adaptationWhen applying the uniform adaptation strategy, an agent adjusts each of its extraction levels by the same magnitude (Delta qleft(a,sright)equivDelta overleftarrow{q}(a)/mleft(aright)) (Fig. 1c). Assuming again that the rate at which an agent enacts this update is proportional to the associated marginal payoff, an agent adapts its extraction levels at all of its affiliated sources (s) by$$q_{t + 1} left( {a,s} right) = q_{t} left( {a,s} right) + kleft[ {alpha – beta overline{chi }left( a right) – gamma {mathop{q}limits^{leftarrow}}_{t} left( a right)} right],$$
(6)
where (overline{chi }left( a right) = left[ {mathop sum nolimits_{{s^{prime} in {mathbf{S}}_{a} }} chi left( {s^{prime}} right)} right]/mleft( a right)) is the mean state of the agent’s affiliated sources.ReallocationWhen practicing reallocation, an agent shifts an increment of extraction effort from a depleted source to a viable source such that its overall individual extraction (mathop{q}limits^{leftarrow} left( a right)) remains unchanged (Fig. 1d). The agent thus randomly selects one depleted source (s_{{text{D}}} in {mathbf{S}}_{a}) and one viable source (s_{{text{V}}} in {mathbf{S}}_{a}), if available. Since the marginal payoff per unit reallocated is (beta), updates its extraction levels such that$$q_{t + 1} left( {a,s} right) = left{ {begin{array}{*{20}c} {q_{t} left( {a,s} right) – kbeta , } & {{text{if}} s = s_{{text{D}}} } \ {q_{t} left( {a,s} right) + kbeta , } & {{text{if}} s = s_{{text{V}}} } \ {q_{t} left( {a,s} right),} & {text{otherwise }} \ end{array} } right.$$
(7)

When an agent’s affiliated sources all share the same quality value, no such reallocation is possible, and so the agent retains its present extraction levels: (q_{t + 1} left( {a,s} right) = q_{t} left( {a,s} right)) for all (s in {mathbf{S}}_{a}).Mixed strategiesAn agent’s adaptation strategy (({p}_{0},{p}_{updownarrow },{p}_{leftrightarrow })) comprises the probabilities that it will practice each of these update rules in any given round: its free adaptation propensity (({p}_{0})), its uniform adaptation propensity (({p}_{updownarrow })), and its reallocation propensity (({p}_{leftrightarrow })). An agent’s choice of a particular update rule is thus based only on its own innate inclinations, but the rate at which it enacts the selected rule is influenced by current resource conditions. We first simulate dynamics in which the same adaptation strategy is shared by all members of a population throughout the entire course of a simulation. We then consider games in which agents’ individual adaptation strategies are each allowed to independently evolve under generalized reinforcement learning38,43 (Supplementary Information S1.3.4). That is, after enacting a chosen update rule in an iteration (t), each agent (a) observes the payoff change (Delta {f}_{t}left(aright)={f}_{t}left(aright)-{f}_{t-1}(a)). If (Delta {f}_{t}left(aright) >0), then the agent’s relative propensity to practice this update rule in subsequent rounds is increased. If the agent’s payoffs decreased ((Delta {f}_{t}left(aright)0) or remediation threshold ({overrightarrow{q}}_{mathrm{R}}left(sright)). That is, all resource depletion events are assumed to be extreme enough to motivate agents to continuously “self-regulate” by remediating depleted sources (see Supplementary Information S5 for a more thorough discussion of these parameter settings).In simulations where reinforcement learning is applied, all agents are initialized with ({p}_{updownarrow }={p}_{leftrightarrow }=.333). For pure free adaptation simulations (({p}_{0}=1)), initial extraction levels were randomized (({q}_{t=0}left(a,sright)in [0,frac{{overrightarrow{q}}_{mathrm{D}}left(sright)}{nleft(sright)}])). All other simulations (({p}_{0} More

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