Identifying potential consequences of natural perturbations and management decisions on a coastal fishery social-ecological system using qualitative loop analysis

Managing for sustainable development and resource extraction requires an understanding of the feedbacks between ecosystems and humans. These feedbacks are part of complex social-ecological systems (SES), in which resources, actors, and governance systems interact to produce outcomes across these component parts. Qualitative modeling approaches offer ways to assess complex SES dynamics. Loop analysis in particular is useful for examining and identifying potential outcomes from external perturbations and management interventions in data poor systems when very little is known about functional relationships and parameter values. Using a case study of multispecies, multifleet coastal small-scale fisheries, we demonstrate the application of loop analysis to provide predictions regarding SES responses to perturbations and management actions. Specifically, we examine the potential ecological and socioeconomic consequences to coastal fisheries of different governance interventions (e.g., territorial user rights, fisheries closures, market-based incentives, ecotourism subsidies) and environmental changes. Our results indicate that complex feedbacks among biophysical and socioeconomic components can result in counterintuitive and unexpected outcomes. For example, creating new jobs through ecotourism or subsidies might have mixed effects on members of fishing cooperatives vs. nonmembers, highlighting equity issues. Market-based interventions, such as ecolabels, are expected to have overall positive economic effects, assuming a direct effect of ecolabels on marketprices, and a lack of negative biological impacts under most model structures. Our results highlight that integrating ecological and social variables in a unique unit of management can reveal important potential trade-offs between desirable ecological and social outcomes, highlight which user groups might be more vulnerable to external shocks, and identify which interventions should be further tested to identify potential win-win outcomes across the triple-bottom line of the sustainable development paradigm.


INTRODUCTION
Mounting evidence of ecosystem degradation and the resulting reciprocal effects on human well-being have led to calls for comprehensive ecosystem-based management worldwide.Natural resource management has moved away from approaches that focus on a single species or sector, view the environment as static, and separate social and ecological issues toward integrated, dynamic approaches that consider the entire ecosystem, including humans, interactions among social and ecological components, and the cumulative impacts of multiple activities (Hughes et al. 2005, McLeod et al. 2005, Leslie and McLeod 2007, Levin et al. 2009).This shift reflects the view that managing for sustainable development and resource extraction requires an understanding of the feedbacks between biophysical systems and humans, and thus requires an integrative, interdisciplinary approach.These feedbacks are part of social-ecological systems (SES), in which resources, actors, and governance systems interact to produce outcomes across these component parts (Berkes and Folke 1998, Ostrom 2009, Cox et al. 2010, McGinnis and Ostrom 2014).
Marine ecosystems and the fisheries they support are examples of complex SES, with numerous relationships among ecological, social, economic, and institutional components operating at multiple scales (Berkes 2006, Mahon et al. 2008, Levin et al. 2009, Berkes 2011, Halpern et al. 2012, Kittinger et al. 2013).Governance and financial systems interact with social systems to influence human behaviors, which in turn have an impact on the marine and coastal environments, while the marine environment and resource units can in turn influence the choice of operational and collective-choice rules, and economic and cultural values (Fig. 1).All of these elements interact to produce a set of dynamic outcomes (Berkes andFolke 1998, Mahon et al. 2008, Ostrom 2009, McGinnis andOstrom 2014).Current marine resource management recognizes the importance of considering interactions among fisheries components to meet social, ecological, and economic sustainability, but it can be challenging to develop an explicit understanding of the direct and indirect effects of fisheries on the larger web of interacting species and the feedbacks among these components on the greater socialecological network.The processes to be quantified and modeled are numerous and produce feedbacks whose effects are difficult to predict.These complex dynamics often exceed our current understanding and data availability.However, to inform decision making and guide future monitoring and management actions, managers must evaluate the consequences of management actions or of external perturbations to the system (e.g., drivers associated with climate change, market fluctuations) on the full SES to avoid unintended consequences and to adaptively manage.
A suite of modeling frameworks have been developed to examine biological and human responses to multiple external and internal drivers within coupled SES (MIMES, Boumans and Costanza 2007;InVEST, Nelson et al. 2009;Atlantis, Fulton et al. 2011).Most of these models require large amounts of data because system components are numerous and feedbacks are complex.An alternative to an in-depth, quantitative description of SES and http://www.ecologyandsociety.org/vol22/iss1/art34/Fig. 1.The fishing cooperatives of the Vizcaino region in Baja California Sur, Mexico: (a) map of the study area showing location along the coastline from Punta Eugenia to Laguna San Ignacio; (b) conceptual representation of the social-ecological system (SES) based on the updated SES framework presented in McGinnis and Ostrom (2014).their dynamics is qualitative modeling.Qualitative modeling approaches, including fuzzy cognitive mapping (Kok 2009), causal loop diagrams (Lane 2008), Bayesian belief networks (Woolridge and Done 2004), and loop analysis (Puccia and Levins 1986), can provide practical tools for evaluating external perturbations and management strategies, particularly under circumstances of limited data availability and uncertainty in the nature and strength of relationships within and between socioeconomic and biophysical components (Fishwick and Luker 1991, Dambacher et al. 2007, Espinoza-Tenorio et al. 2013, Carey et al. 2014).Furthermore, they can be developed using participatory approaches with multiple stakeholders and have conceptual appeal, are intuitive, and represent good communication tools.Loop analysis is one particular technique that allows for investigations of the dynamics of complex systems when the signs of interactions are known but other aspects of the linkages are uncertain, including strength of the interactions and their functional forms and parameters; in other words, whether a system component (e.g., species, actors, or user groups) has a positive, negative, or no effect on another component with which it interacts.Despite its limitations (see discussion of merits and limitations in Justus 2006), the limited data requirements of loop analysis make it a promising tool for investigating the dynamics of SES in data poor systems.
Loop analysis allows for an examination of how an external press perturbation (Bender et al. 1984) would potentially spread its effects in a system across multiple socioeconomic and ecological variables through the network of interactions among the variables.In loop analysis, linkages between variables are representations of the directional effect that one variable has on the rate of change of the other.For example, for predator-prey relationships, an increase in a predator population leads to a decrease in the growth rate of its prey.These linkages are expressed mathematically by the coefficients of the Jacobian matrix of a system of differential equations.The sign of these coefficients identify how any one variable qualitatively affects the others.By following the direction of links one can reconstruct the pathways of interactions through which management actions or natural perturbations propagate beyond the target variable.The abundance or level of any of the variables in the system may be predicted to increase, decrease, or remain the same following the natural perturbation or management intervention.
Thus, loop analysis offers alternatives to quantitative modeling for dealing with the complexities of SES in data poor systems and provides testable hypotheses regarding SES responses to perturbations and/or management actions (e.g., Carey et al. 2014).Although loop analysis offers an analytical framework for investigating the complexity of marine social-ecological systems (Espinoza-Tenorio et al. 2013, Carey et al. 2014, Reum et al. 2015), many applications of this approach to date have focused on the ecological elements of the system and have not included aspects of the social system and key SES linkages (but see Dambacher et al. 2007).
We apply qualitative loop models to examine changes in coastal SES of the Vizcaino Peninsula, Baja California, Mexico, in response to natural perturbations and management actions that have recently been implemented or are currently under consideration.These coastal fisheries are particularly relevant as a model system because fishing cooperatives of this region were granted exclusive access rights to a suite of invertebrate species starting in the 1930s (McCay et al. 2014), whereas fishing for finfish or by fishermen that do not belong to cooperatives has remained open access.Thus, this system allows for an examination of the ecological and socioeconomic consequences of allocating access rights for different species and to different users (e.g., http://www.ecologyandsociety.org/vol22/iss1/art34/Pomeroy et al. 2001, Costello et al. 2008), a management approach that is currently being implemented in small-scale fisheries globally (http://www.bloomberg.org/program/environment/vibrantoceans/).
Using a case study of multispecies, multifleet, coastal, small-scale fisheries, we demonstrate the application of loop analysis to examine interactions among ecological and socioeconomic variables associated with territorial user right fisheries (TURF)managed commercial fisheries and to understand the main feedbacks that drive the social and ecological performance of these coupled systems.We demonstrate how loop analysis can be applied as a method for examining potential outcomes from scenario analysis to inform planning and monitoring in SES.Through this approach, we examined a set of scenarios that mimic perturbations to the SES including the effects of climate perturbations that have recently been associated with observed decline in different stocks (e.g., Micheli et al. 2012), market-based initiatives such as an ecolabel, which was awarded to one of the fisheries (the spiny lobster trap fishery) operating in this region (Micheli et al. 2014a), and of changes in fisheries management and governance that are currently under consideration (Micheli et al. 2014b).Although these scenarios are designed to capture perturbations and management actions specific to the Vizcaino fisheries, they represent impacts faced by many coastal fishing communities worldwide and management options available to several of these communities.Because the application of loop analysis is relatively novel in the field of fisheries management (but see Espinoza-Tenorio et al. 2013, Carey et al. 2014), we emphasize, through the analysis of realistic scenarios in a case study system, the potential of loop analysis to evaluate complex social-ecological systems.Our analysis should provide useful insights for a suite of small-scale fisheries, in addition to the Vizcaino region cooperatives, to identify hypotheses and key variables for monitoring.Specifically, we ask: (1) What are the anticipated biological and socioeconomic consequences of external perturbations that result in the decline of specific stocks?(2) What market-based, governance, or local management actions may result in both biological and socioeconomic benefits?Which of these actions may result in resource declines or negative socioeconomic impacts?(3) How does the representation of the system (i.e., what specific linkages and feedbacks among system components are included) influence the predicted responses to perturbations?

Study system/conceptual model
To illustrate and describe the components, linkages, interactions, and potential outcomes of the Vizcaino fisheries system, we developed a conceptual model based on Ostrom's socialecological system (SES) framework (Ostrom 2009, McGinnis andOstrom 2014), available literature describing the system, and the authors' knowledge of the system (Martone 2009, Shester and Micheli 2011, Micheli et al. 2012, 2014b, McCay et al 2014;Fig. 1).Components are organized as resource units, which interact among themselves and are part of a larger resource system that is subject to external forces that can influence the system, such as market or other socioeconomic drivers and global environmental change.The governance system defines a set of rules for a set of actors, some of whom are resource users.These systems and their components then interact in different ways to produce social and ecological outcomes.Finally, we indicate related drivers and conditions that are external to the system but which influence the components and their interactions.

Resource System
The study cooperatives are located along the Vizcaino Peninsula of the Pacific coast of central Baja California, Mexico, a region known as the Pacifico Norte (Fig. 1).The Pacifico Norte region can be characterized as temperate to subtropical, with sea surface temperatures ranging from 12-27 °C throughout the year.The region is a mosaic of rocky reef and sandy subtidal ecosystems that encompass the southern edge of the range of giant kelp (Macrocystis pyrifera) in which a zone of persistent upwelling maintains high biological productivity (Martone 2009).

Governance
The cooperatives belong to the Federacion Regional de Sociedades Cooperativas de la Industria Pesquera de Baja California (FEDECOOP), which acts as a comanagement agency with the national and regional fisheries agencies to monitor resources and develop management plans.The fishing cooperatives of the Pacifico Norte date back to the late 1930s, as a manifestation of the Mexican cooperative movement that was mainstreamed into national fisheries development policies (Ponce-Díaz et al. 2009, McCay et al. 2014).From the beginning of the cooperatives, access to high-value fisheries, such as lobster (Panulirus interruptus) and abalone (Haliotis spp.), in adjacent fishing grounds has been restricted by law to cooperative members.Since 1992, this special right has been in the form of 20-year concessions for exclusive exploitation rights for some species, including lobster and abalone.
The long-term exclusive concessions held by the cooperatives are examples of the assignment and comanagement of communitybased access, withdrawal, exclusion, and management rights (Schlager andOstrom 1992, Pomeroy et al. 2001).These community-based access rights have enabled cooperatives to add and enforce conservative management measures, including, but not limited to, regulation of catch composition, seasonal closures, and size limits in lobster fisheries (Vega 2001), reef-specific quotas, and the voluntary establishment of no-take reserves exclusively aimed at rebuilding abalone populations and other fisheries targets (Micheli et al. 2012, McCay et al. 2014).Both cooperative and noncooperative members are compliant with rules because of both positive and negative incentives that come with membership in the cooperative and ongoing investment in monitoring, enforcement, and infrastructure (McCay et al. 2014).However, the lack of concessions and associated rights for finfish may impede management of these stocks in this region, given that the incentives that often accompany comanagement and exclusionary rights are not in place for these species (Shester andMicheli 2011, Micheli et al. 2014a).

Resource Units
The Pacifico Norte fisheries target a wide variety of interacting species in rocky reef food webs, including predators, such as lobster and several finfish species, and their prey and competitors.Currently, in addition to lobster and abalone, cooperatives have exclusive rights to a set of other benthic species, including the wavy turban snail Megastraea undosa, the sea cucumber Parastichopus parvimensis, the red sea urchin Mesocentrotus http://www.ecologyandsociety.org/vol22/iss1/art34/franciscanus, and the red alga Gelidium robustum.The cooperatives also catch finfish, primarily barred sand bass (Paralabrax nebulifer), ocean white fish (Caulolatilus spp.), and California halibut (Paralichthys californicus) using nets and traps.In contrast with benthic invertebrates and algae, cooperatives do not hold territorial rights for finfish, so fishermen that are not members of the fishing cooperatives also have access to these species.

Actors
The FEDECOOP fisheries are located on the coastal edge of a vast desert protected by UNESCO biosphere reserve designation since 1988 (Fig. 1).The remote nature of these fisheries in combination with their unique institutional structure and history of occupation along the coast leads to the cooperatives playing a strong role in the community.Collectively, the cooperatives provide infrastructure, social programs, and employment to many residents in the communities, including both cooperative members and nonmembers, in jobs involving harvest, rule enforcement, resource monitoring, seafood processing, and transportation (Ponce-Díaz et al. 1998;Fig. 1).

Socioeconomic and ecological interactions and outcomes
Membership in the cooperatives brings social and economic benefits.Abalone and lobster are the main targets and provide high value to the cooperatives because of high demand and market prices for these commodities (McCay et al. 2014).Finfish fisheries are also economically important in the region, representing additional, and in some cases the most important income source for cooperatives (Shester and Micheli 2011).Moreover, opportunities to engage in finfish fishing provide additional income for cooperative members during the closed fishing season for their main target species, as well as income and subsistence harvest for noncooperative members in the community, who do not have access to benthic fishery targets that are the purview of the cooperatives (Shester and Micheli 2011).However, despite delivery of important benefits to cooperative members and nonmember fishers, the gear types used by this fishery tend to have higher by-catch rates and may have adverse long-term effects on target populations, food webs, and habitats (Shester andMicheli 2011, Micheli et al. 2014a, b).

Loop analysis
The loop analysis first translates the conceptual model (Fig. 1) into a pictorial representation of interactions between the SES components, including resource units (e.g., species, fisheries catch), actors (e.g., cooperative members and noncooperative fishers), the governance system (e.g., harvest control rules, fishing effort), and socioeconomic factors (e.g., income, jobs for noncooperative members; Fig. 2).We assembled the SES interaction web capturing some of the main biological and socioeconomic components in our conceptual model (Fig. 1) and illustrated the linkages among them in a signed diagraph (Fig. 2; Appendix 1).We represent biological linkages as possible trophic relationships among target species or species groups, the linkages among species and fisheries operating in the study region based on harvest control rules, and key actors and some relevant socioeconomic components of the system (Fig. 2).The interaction web was assembled based on authors' experience and knowledge of the system and from relationships described in the published literature, including data from sampling and taxonomic identification of the benthic fauna and flora, stomach content analyses of fish and invertebrates, interviews with fishermen and cooperative members, and household surveys (Shester 2008, Martone 2009, Morales-Zárate et al. 2011, Ramírez-Sánchez et al. 2011, Shester and Micheli 2011, McCay et al. 2014, Leslie et al. 2015).The main model (model 1) includes predator-prey relationships among the three stocks, abalone, lobster, and finfish, and negative relationships among fishing effort between the abalone and lobster fisheries and the lobster and finfish fisheries.The other four model structures are variations on this primary model and remove some of the linkages among fishing efforts (models 2-5).
Loop analysis qualitatively predicts average changes in variables of interest (e.g., species abundance or catch) in response to varying conditions that modify their rate of change, i.e., variations in parameters governing the rate of change for the variables.One example is a stressor that increases the mortality rate of a species.This reduces that species' population growth rate, which in turn influences the abundance of that species as well as that of the other species to which the latter is connected in the network.The variation in the level of a component j due to a parameter change can be calculated by the loop formula: where c is the changing parameter (e.g., mortality, fecundity, predation rate); ∂fi /∂c designates whether the growth rate of the http://www.ecologyandsociety.org/vol22/iss1/art34/i-th variable is increasing, decreasing (positive or negative input, respectively); p ji (k) is the pathway connecting the variable that undergoes parameter change, i, with the variable whose equilibrium value is being calculated, j, and which includes k variables; F n-k (comp) is the complementary feedback, which buffers or reverses the effect of the pathway.The denominator indicates the overall feedback of the system, which is a measure of the inertia of the whole system to change.A more detailed explanation of the method of loop analysis and the algorithm for predictions is given in Appendix 1. Loop analysis models were run in R using a code that is provided in Appendix 2.

Biological links
For our resource units, we included three main target species and species complexes in our loop analysis: lobster stocks, abalone stocks, and finfish stocks.We represent the following biological interactions in the social-ecological system: lobster are known predators of molluscs including abalone (Braje et al. 2009); finfish, such as gulf grouper (Mycteroperca jordani), cabezon (Scorpaenichthys marmoratus), and sheephead (Semicossyphus pulcher), are predators of both lobster, particularly the juvenile stages, and abalone (Braje et al. 2009;Fig. 1).Thus, abalone (AS), finfish (FS), and lobster (LS) form a tri-trophic system: FS preys upon both AS and LS, while LS preys upon AS.All stocks have negative feedback loops to themselves, representing densitydependent effects on population growth rate.Because these predators are all generalists and the degree to which these interactions drive top-down or bottom-up processes are unknown in this system, we tested the effects of including these interactions in the network in three different models, including top down and bottom up effects, bottom up effects only, and no biological interactions.This latter case explores the situation in which the biological interactions are completely obscured by socioeconomic links in determining the dynamics of fish variables.

Fisheries links
The Pacifico Norte cooperative fisheries target lobster using traps, abalone using hookah diving, and finfish using a variety of gear types, including traps, set gillnets, and driftnets (Shester andMicheli 2011, Micheli et al. 2014b).As in most fisheries, we assume that stock and effort have positive effects on catch, catch has a negative effect on stock, and effort and stocks have negative effects on each other (Fig. 2).The negative link from stock to effort considers that the larger the stock, the lower the effort required to obtain the same catch.Factors that control the fisheries are translated in the model as a self-damping term on effort and catch, representing the action of other variables that are not included in the model but can regulate model components (Bodini 1988).Although several factors, beside the densitydependent mechanism, can generate a self-damping term on variables (Puccia and Levins 1986), we do not include this mechanism in all of our variables, because the inclusion of all variables that play a regulative effect on the system in the model would make the model intractable.Because these fisheries are all conducted under the same cooperative system by the same fishers, and abalone and lobster are the main cooperative targets, we have linked effort among fisheries, such that both lobster and abalone effort negatively affect the rate of change of finfish effort, and abalone effort is negatively linked to lobster effort.We tested the effects of including these linkages on the outcomes of the SES by varying our model structure (Fig. 2).
In addition to the linkages among fishing efforts within the cooperatives, there are also nonmembers that have access to finfish stocks because the cooperatives do not hold exclusive access privileges for finfish.We captured nonmember effort separately by linking it negatively to the same finfish stock that is targeted by the cooperatives (Fig. 2).Nonmember effort is positively linked to nonmember finfish catch and is negatively linked to finfish stock size (Fig. 2).

Socioeconomic links
Both cooperative members and nonmembers gain income directly from the catch of stocks.Therefore, nonmember finfish catch positively affects nonmember income, whereas finfish, abalone, and lobster catch all positively affect member income (Fig. 2).In all of our models, income negatively affects effort.Furthermore, to capture the positive effect that cooperatives have on nonmembers in these communities through the provision of job opportunities (e.g., in seafood processing plants), member income positively affects job opportunities in the community and jobs positively affect nonmember income (Fig. 2).

Predicting change through loop analysis
The loop formula (1) allows predictions of how the level of system components might change because of external forcing (Puccia and Levins 1986).Predictions calculated with the loop formula can be arranged in a table with signs showing the expected direction of change (+, -, or 0).In Figure 3, signs for predictions are substituted by arrows for a clearer presentation.The entries in the table denote variations expected in the column variables when positive parameter inputs affect each row variable.Each row of the table indicates the variable that is subjected to parameter change.The responses of the variables to variations in the rate of change of a given row variable are reported in the columns.These responses concern the direction of change of the level of the variables (e.g., biomass, number of individuals, or amount of money).Predictions are conventionally obtained for positive input.In the case of a negative input, predicted directions of change along the row of interest are simply inverted.
Model variables are often connected to each other by multiple pathways.If such pathways have opposite effects, the model can yield ambiguous predictions.In these cases, model predictions are undetermined, and + or -signs in the table of predictions are replaced by question marks (?).To address these ambiguous predictions, we used a routine that randomly assigns numerical values to coefficients of the community matrix (i.e., the coefficients of the links in the signed digraph).Values for links are generated randomly by a routine within the interval (10 -6 -1).This procedure is executed n x n x 100 times, where n is the number of variables in the model.Therefore we created for each model community matrices (n = 14; Total runs = 19,600).Community matrices can then be inverted to understand how variables affect each other directly and through indirect pathways (Bender et al. 1984, Wootton 2002, Montoya et al. 2009).The coefficient (cij -1 ) of the inverse community matrix shows the overall effect of variable j on variable i due to its direct link to variable i (e.g., predation, catch), as well as all possible indirect pathways through which variable j is connected to i via intermediate components.
Hence, the net effect (the sum of the direct and indirect effects) of a perturbation on variable j on variable i is given by the element of the inverse community matrix. .Zeros (yellow dots) reflect compensation between positive and negative effects that result from the model runs and likely no change would be expected in the variable's level.Predictions are obtained by assuming positive inputs (i.e., increased rates of change of the variables) to the row variables.Predictions for negative inputs (decreased rates) can be easily obtained by simply inverting the direction of the arrows and of the triangles (and the colors).The first letter of the variable labels (in the rows and columns) identifies a system component (e.g., A for abalone, L for lobster, F for finfish), the second letter a specific descriptor of that component (e.g., S for stock size, E for effort, C for catch; see Figure 2 legend for a complete list of the variables and their acronyms).
The community matrix AH must have a nonzero determinant and must admit an inverse matrix (AH) -1 .Of the n x n x 100 matrices created for each model, only those that satisfied the Lyapunov conditions of stability were kept and inverted.An overall table of predictions for each model was then obtained from the inverted matrices.In this table, each prediction was determined on the basis of the percentage of positive, negative, or zero signs in the array of the inverted stable matrices (Appendix 1, Table S2).We defined a set of rules to translate the percentage of cases obtained from loop analysis runs into signs in the overall prediction matrix (Puccia and Levins 1986).Specifically: -indicates that 0-25% of the relationships were positive; ?-indicates 25-40% of the relationships were positive; 0* indicates 40-60% positive change relationships; ?+ indicates 60-75% of linkages were positive; and a + indicates 75-100% of the signs obtained in the procedure were positive.This is based on Puccia's 3:1 ratio rule (Puccia and Levins 1986).Note that 0* are not real zeros but a neutral result that occurs when matrices have large numbers of opposite signs for a given variable's response.In fact, when multiple pathways have opposite effects to the same variable, positive and negative effects tend to compensate each other and the net result may be zero (no variation) or, more likely, a small change, which can be reasonably considered negligible.

Model structure and scenario testing
We examined the system dynamics and behaviors by conducting two different types of analyses.First, we explored the effects of different assumptions about model structure, particularly which linkages between variables are included or excluded (five model structures).Second, we investigated the system responses to perturbations (considering seven different perturbation scenarios).
To examine the sensitivity of model results to the specific linkages included, we varied model structure by including or removing different sets of biological and/or fisheries linkages.Models 1-5 (Fig. 2; Appendix 1, Table S2) include all of the biological linkages, in which both effects of predator and prey are represented, but each model varies the relationships among fishing effort, including or removing hypothesized links between abalone and lobster fisheries, lobster and finfish fisheries, and abalone and finfish fisheries.
We also varied the core biological structure to examine the robustness of outcomes to different assumptions about how species may affect each other through consumer-resource interactions.In a second set of models, we removed all biological linkages and varied the relationships among fishing efforts, as described above for models 1-5.In a third set of models, we included biological links but only in the form of the beneficial effect that prey exerts upon its predator, i.e., a bottom-up effect of resources on consumers.In all of these cases, the models yielded a zero matrix determinant and no predictions could be obtained.This means that the full set of biological interactions is needed for models to generate meaningful predictions.Thus, we present and discuss results only for models 1-5 (Fig. 3; Appendix 1, Table S2).
We investigated responses of single variables to parameter changes in the system by examining: (a) the table of predictions for each model to explore what relationships emerge between the ecological and socioeconomic components, and within the three fisheries; and (b) seven scenarios associated with specific external perturbations and management actions to examine the response of variables of interest, both biological (stock abundance) and socioeconomic (jobs, income).http://www.ecologyandsociety.org/vol22/iss1/art34/Environmental perturbations Disease, hypoxia, and climate change are major drivers of change in marine ecosystems and are associated with increased mortality of fisheries species in many coastal fisheries (Defeo andCastilla 2012, Micheli et al. 2012).In scenario 1, we simulated the external forcing of climate or other human impacts through decreased growth rate of abalone.Hypoxia, frequent or extreme El Nino-Southern Oscillation (ENSO) events, disease, or harmful algal blooms underlie observed abalone declines and may lead to further decline by increasing abalone mortality (Morales-Bojórquez et al. 2008, Micheli et al. 2012).In scenario 2, we modeled effects of disease or ocean acidification impacts on lobster populations as a negative input to lobster stocks, reflecting an increase in lobster mortality or a decrease in lobster growth and reproduction from these external drivers.Studies of the effects of ocean acidification on crustaceans indicate likely negative impacts on growth due to rises in [H+] in haemolymph and reduced oxygen delivery to the tissues (see Whiteley 2011 for review).Although disease has not affected lobster stocks in this system, it is a major concern for other lobster fisheries (e.g., Steneck et al. 2011).

Socioeconomic drivers
We examined the effects of market-based initiatives, such as the existing Marine Stewardship Council (MSC) ecolabel or proposed system-wide certification schemes that are implemented with the goal of increasing income to the fishing cooperatives (Micheli et al. 2014a).We modeled these drivers in scenario 3 as positive inputs to the cooperative member income, although in the case of the Vizcaino cooperatives, although the eco-label allows for some increased access to higher prices in the US market, it primarily functions as a source of empowerment and helps the cooperatives maintain their concessions (Pérez-Ramírez et al. 2012a, b).Other initiatives have been proposed for this region with the aim of increasing job opportunities for noncooperative members, such as abalone pearl culture and ecotourism.In scenario 4, we tested the effects of change to nonmember income through these opportunities accessible to nonmembers of cooperatives, designed to provide alternatives to fishing.

Fisheries management actions
Though not yet implemented, decreasing finfishing effort and phasing out of set gillnets has been highlighted as a possible option for decreasing the environmental impacts and improving the long-term sustainability of these cooperative fisheries (Peckham et al. 2007, Shester and Micheli 2011, Micheli et al. 2014b).In scenario 5, we examined how these management actions would influence other variables in the system using a negative input to cooperative member finfish effort.In scenario 6, we examined the effects of controls on nonmember finfish effort on the system.Finally, in scenario 7, we examined the effects of increased job opportunities through subsidies provided by the government, private foundations, or NGOs.

Sensitivity analysis
To examine whether model structure affected outcomes, we compared the tables of predictions from the five models to see whether there was concordance among them.We compared each prediction matrix, for each model, to all other matrices in a series of pairwise comparisons and determined the number of cases in which each prediction matrix differed from all others (Appendix 1, Table S3).

Model predictions: social-ecological systems (SES) dynamics
Loop analysis reveals that changes in input variables (e.g., stocks' growth rates, rate of change in member income) may influence other variables in the system in directions that often cannot be predicted based on known (or assumed) directional relationships.For example (see Fig. 3), an increase in the abalone growth rates (positive input to AS) is predicted to reduce lobster stock, which is counter to the notion that prey species should positively influence the abundance of their predators.This is because the influence of a variable on any other is mediated by the other variables in the system through indirect effects.
Another surprising outcome is changes in predators leading to no effects on their prey.The correlations between predators and prey vary depending on which stock is perturbed, because of feedbacks and compensation throughout the SES.For example, when the finfish stock's (FS) growth rate increases, FS itself is predicted to increase, but abalone stock (AS) does not change (Fig. 3).This result could be interpreted as a result of FS preying upon AS but also on LS, which, in turn preys upon AS.So the effect of FS on AS is at the same time positive and negative because this species also feeds on a predator of AS.However, the complexity of the SES increases the multiplicity of the pathways that connect FS and AS.The loop analysis indicates that FS is connected to AS by eight paths: four paths with a negative sign and four positive (the product of the signs of the links yield the overall sign for the path; see Appendix 1, Table S1).Thus, our simulations yielded the same percentage of matrices in which AS is expected to increase and matrices in which AS is expected to decrease (50%), resulting in a compensation of effects and a magnitude of variation that can be close to zero.
A positive input on FS causes lobster stock (LS) to decrease.This negative effect that LS experiences when a positive input affects the growth rate of FS could be due to the direct predation on LS and the predation on its prey.However, in a complex system like the one we describe in Figure 2, any effect of one variable on another is mediated by multiple pathways, so the full set of pathways must be examined to understand the effects.
Nine pathways connect FS to LS (Fig. 2; Appendix 1, Table S1).Five carry a negative effect to LS and four carry a positive effect.Although there is only one additional path indicating negative effects of FS on LS, the numerical simulation yielded that only 8% of the matrices predict an increase for the level of LS with a positive input affecting FS.But 91% of the matrices predict the population of LS to decrease following a positive input to FS.This is surprising, given that with the quasi-balanced number of pathways carrying opposite effects, we would expect the results of the simulation be more equilibrated.Likely this discrepancy between what we would expect looking at the number of pathways and what we obtain from the simulations depends on the following: random coefficients are taken in the range 10 -6 -1, but the product of link values in longer paths yields smaller numbers than the shorter paths; so that these latter contribute more to the final outcome from the loop analysis.If we consider the pathways from FS to LS (Appendix 1, Table S1), the two shortest pathways both have negative signs and we can understand why despite the numerical quasi-balance between opposite pathways, the response of LS to an increase in the growth rate of FS is negative.http://www.ecologyandsociety.org/vol22/iss1/art34/In the previous case (input to FS and effect on AS), instead, the two shorter paths (Appendix 1, Table S1) have opposite signs.This relationship between FS and LS is consistent with what is anticipated from known predator-prey relationships, with some of the finfish species targeted by local fisheries (e.g., sheephead, S. pulcher) preying on lobster (i.e., an anticipated negative effect of increased FS on LS).
Despite expected negative effects on AS from FS and LS as predators, a positive correlation emerges between AS and FS when there is a perturbation to AS, whereas either no correlation or a negative correlation is predicted between AS and LS.As inputs enter the system through lobster stock (LS), LS becomes negatively correlated with AS, whereas no correlation exists between these two variables and FS, the abundance of which in all five models is predicted not to change.
The table of predictions can be used as a diagnostic tool to detect the entry point(s) of perturbations.For example, abalone stock (AS) changes only if perturbations enter the system through the abalone and lobster fisheries in the form of input to stocks and effort for both these fisheries.The only exception is model 4 (Appendix 1, Table S2), in which input to effort on finfish by members of the cooperative (ME) is predicted to affect abalone stock.According to these results, any variation in AS can be associated to alterations in the abalone or lobster fisheries but not in other variables of the system (i.e., economic variables).
Examining relationships between the fishery variables (catch, effort, and stocks) can also provide insights in the dynamics of specific fisheries.For example, the 3 x 3 submatrix that includes the relationships among variables AS, AE, and AC (abalone stock, fishing effort, and catch; Fig. 3) can be examined to glean information about aspects of the abalone fishery.As expected, abalone stocks are negatively correlated with effort: as effort increases, stock decreases and vice-versa.Effort and catch are positively correlated in one direction but negatively correlated in the other direction: as effort increases, catch increases, but as catch increases, effort is predicted to decrease.However, stock and catch show a neutral relationship, suggesting that effort is the key control variable.This submatrix is identical across all five models that we investigated (Appendix 1, Table S2), suggesting that conclusions based on this submatrix are robust to variations in model structure.
The table of predictions can also indicate which variables are most susceptible to external perturbation, either from environmental change or management interventions.For example, member income (MI) shows a greater inertia than nonmember income (NI) to parameter changes (Fig. 3).In model 1, 8 out of 14 possible responses of MI to external inputs are null (Fig. 3), and this pattern changes only slightly in the other models (the number of zeros varies between 6 and 8; Appendix 1, Table S2).Nonmember income remains unaltered only when inputs enter the system through AE, LS, and ME, in various combinations for the five models.Thus cooperative member income seems less vulnerable to perturbations than nonmember income, but it is also predicted to be less responsive to management interventions.

Collapse of target taxa (scenarios 1 and 2)
Disease and climate change are indicated as major drivers of increased mortality of target species and fisheries collapse.In scenario 1, we modeled the impacts of a disease, extreme ENSO, harmful algal blooms, or hypoxic events affecting abalone (Shepherd et al. 1998, Morales-Bojórquez et al. 2008, Micheli et al. 2012) as a negative input on abalone stock (AS; Fig. 4).Without effective effort control, a reduction in the abalone stock is accompanied by increased effort and no change in catch.However, income for both members and nonmembers is predicted to decrease, so that the increased mortality of abalone results in an overall economic loss for the local community.Biologically, the decline in abalone stocks is accompanied by a decrease in finfish stocks (FS) and an increase in lobster stocks (LS; Fig. 4).Interestingly, finfish effort is predicted to increase for both members (ME) and nonmembers (NE), but finfish catch for both groups (MC, NC) declines (Fig. 4).Job opportunities (JO) remain unaffected under all models.
In scenario 2, we modeled the negative impact of a disease on lobster stocks (Steneck et al. 2011).A negative input on lobster stock is predicted to lead to increases in abalone and no effects on finfish stocks (Fig. 2), assuming that disease would not simultaneously affect abalone and finfish stocks.The models reveal a substantial inertia of the system to lobster stock perturbation because no change is predicted for all other fishery and socioeconomic variables (Fig. 4).These simulations highlight a greater sensitivity of the system to perturbations on abalone than lobster, as suggested by more negative outcomes in scenario 1 than 2 (Fig. 4).
Results for scenarios 1 and 2 are relatively robust to the representation of the interactions in the system because removing links between fisheries through the effort variable does not change the directional responses of the variables (Appendix 1, Table S2).

Market-based interventions (scenarios 3 and 4)
In scenario 3, we examined the effects of the ecolabel, which is represented by a positive input to member income (MI).This is the only scenario that yields predictions of positive outcomes for both biological and economic variables, and for both user groups.Income and jobs are predicted to increase for both members and nonmembers, fishing effort is expected to decrease for all fisheries, abalone and lobster stocks are predicted to remain stable, and finfish stocks to increase (Fig. 4).Thus, improving member income through market-based incentives is predicted to have beneficial effects on the overall economy, with positive consequences on stocks that are either stable (AS and LS remain unchanged) or increase (FS).
In scenario 4, nonmember income is increased through opportunities from tourism development or other income opportunities not associated with fisheries.Under this scenario, benefits would accrue only for nonmembers, whereas member income is predicted to remain unchanged.This intervention would not have an impact on the abalone fishery, as indicated by no changes in AS, AE, or AC.Finfish stocks would increase because of decreased fishing effort associated with economic  5) management decision that leads to decrease in member finfish effort; (6) management decision that leads to decrease in nonmember finfish effort; and, (7) increase in job opportunities (e.g., from subsidies).Outcomes for each variable from each scenario are given for the main model (Model 1, Fig. 2), which includes all linkages of the social-ecological system.Bar graphs indicate the percentage of positive outcomes from the loop analysis model runs.
alternatives, and lobster stock is predicted to decrease as a result of increased abundance of their predators.Thus, the main target stocks and the overall economy are not expected to benefit under this scenario.

Fisheries management actions (scenarios 5, 6, 7)
Management measures put in place to reduce member effort in the finfish fishery (ME) are predicted to lead to negative socioeconomic outcomes for all user groups (scenario 5; Fig. 4).Member and nonmember incomes and jobs are all expected to decrease.Thus, economically, this scenario has the most detrimental outcome among those considered.Finfish catch by members (MC) declines whereas catch by nonmembers (NC) shows a tendency to increase.Different consequences are predicted for abalone (AS) and lobster stocks (LS): LS is expected to decline, whereas AS is predicted not to change.Interestingly AS does not change despite both abalone effort and catch increasing.This highlights the difficulty of predicting outcomes using linear criteria of causation developed by focusing on the separate interactions between stock, effort, and catch in a single fishery.
A reduction in nonmember finfish effort (scenario 6) is also expected to result in economic loss for nonmembers and no income improvement for members.Nonmember income is predicted to decrease, likely due to finfish catch decrease because of reduced effort.Increased fish stocks result in decreased lobster stocks, whereas abalone stock is not affected and the abalone http://www.ecologyandsociety.org/vol22/iss1/art34/fishery seems insensitive to this input.As finfish stock increases, the feedback within this fishery results in constant catch, even with a decrease in effort.This does not hold for nonmembers because both catch and effort decrease.
Increasing the rate of change for job opportunities (scenario 7), for example through external subsidies or investments, leads to limited beneficial effects.As in the previous case (scenario 6), nonmember income is predicted to increase whereas member income would remain stable.Again the abalone fishery seems quite unaffected by this intervention whereas negative consequences are predicted for the lobster fishery (Fig. 4).
We further varied model structure to examine potential outcomes of other management interventions that might influence the system.Specifically, in our models 1-5 we represented the more general case of effort responding to changes in catch and stock, and did not consider regulatory controls that might influence this relationship, assuming that regulatory controls may not always be effective.From trends of catch and effort data on lobster in Baja California from 1960 to 2010 (Vega 2001), two phases can be identified in the historical records.During the first period (from 1970 to approx.1990) effort increased while catch remained more or less constant, and in the second period (from 1995 to 2004), catch increased with constant effort.Predictions from our models indicate that an increase in effort may be accompanied by a constant catch only when we simulate a negative input on lobster stock, such as increased mortality or reduction in recruitment.Outcomes that reflect the second regime, in which a constant effort was accompanied by increased catch, requires a positive input to lobster catch, which may reflect improved catchability through, for example, implementing gear changes.However, during 1995-2004, effort was kept constant in the FEDECOOP cooperatives by maintaining the number of traps and length of the fishing season constant (Vega 2001).To examine how effective control of lobster fishing effort would influence outcomes, we introduced government agency as a controlling variable on lobster effort in additional models (Appendix 1, Table S4).Government agency (GA) is introduced as an external control of LE with no self-damping and with no other links to the rest of the system, so that GA responds to and acts solely on lobster effort (Appendix 1, Fig. S1).Interestingly, the table of predictions indicates that the presence of this variable makes LE resistant to all parameter changes except for input on GA itself (Appendix 1, Table S4).Models predict that increased catch can be obtained only with a positive parameter change on lobster catch, as in the case without control over effort (Fig. 3).In this latter case, a null value represents a true zero response and not compensation due to opposite forces.This zero response is typical of variables that are connected to a satellite variable (Levins 1974, Puccia andLevins 1986).Government agency is a satellite variable because it is connected to the system only through its linkage with LE and taken in isolation represents a system with zero feedback.

Sensitivity analysis
The largest difference in the frequency of predicted signs among the five models considered is between models 2 and 3, which differed in 28% of all pairwise comparisons (Appendix 1, Table S3).On average, comparisons among the five models yielded different signs in 20% of cases.However, if tendencies of signs (i.e., predictions such as ?+ and ?-) are considered as true signs (i.e., ?+ becomes + and ?-becomes -) differences are less pronounced: models 2 and 3 are still the most different but yield different predictions in only 17% of comparisons, and the average difference among models is 12%.Therefore, model structure can affect outcomes, but different predictions are obtained in a small fraction of simulations, suggesting that outcomes can be considered relatively robust to changes in the model structure that we tested.

DISCUSSION
Qualitative modeling approaches provide tools for learning about possible behaviors and responses to interventions in SES (Dambacher et al. 2007, Carey et al. 2014), as exemplified by this application of loop analysis to the coastal small-scale fisheries of the Vizcaino region in Baja California, Mexico.This approach can generate predictions and hypotheses about possible outcomes of management actions, new policies, or environmental drivers, and can highlight crucial links that need to be investigated to better understand the dynamics of complex SES.Loop analysis applied to the SES of coastal Baja California indicates how complex feedbacks among biological and socioeconomic components can result in counterintuitive and unexpected outcomes as a result of external perturbations.In general, our results suggest that possible trade-offs and cascading effects of management actions and new policies should be carefully considered when the goal of management is to simultaneously improve environmental condition and livelihoods of different user groups (Levin et al. 2009, Carey et al. 2014, Micheli et al. 2014a).Our results are consistent with broader scale analyses of Baja California smallscale fisheries applying the SES frameworks, which have highlighted trade-offs in achieving ecological and social sustainability, and high variability among different geographic regions of the Baja California Peninsula (e.g., Leslie et al. 2015).
Loop analysis helps highlight which components of ecosystems might be more or less vulnerable to perturbations and which interventions may be more beneficial than others for different components of the ecosystem and user groups.Our analysis of possible future scenarios of environmental or management change indicate that, under our assumptions for how system components interact, lobster stocks are predicted to be most vulnerable whereas finfish stocks are expected to benefit under most scenarios.Abalone populations appear to be generally insulated, showing relatively high resistance to changes in other components according to most scenarios.However, mass mortality of abalone (scenario 1) is predicted to have negative effects on catch and income for different user groups, with overall more negative outcomes than, e.g., disease or environmental conditions causing lobster mortality.In other words, abalone stock is rather insensitive to changes in other variables but changes in abalone's rate of change are likely to influence the whole system.Our models also show a negative correlation between lobster and finfish stocks.This negative correlation suggests that attempts to restore one of the two stocks or increasing its growth rate will negatively affect the other unless interventions are targeted to few variables (i.e., AC, LS, LC, ME, MI).These hypotheses need to be tested and should be carefully considered before management intervention.

Models produced specific predictions about the possible socioeconomic outcomes of different interventions or perturbations, and highlight what management interventions
might be most beneficial or most detrimental to the local economy.http://www.ecologyandsociety.org/vol22/iss1/art34/Only scenario 3, the ecolabel, shows positive effects on all three socioeconomic variables considered, i.e., member and nonmember income and jobs.The other six scenarios yield less positive outcomes for the economy of the system, where most predictions are negative (e.g., mass mortality affecting abalone stocks, the most valuable resource in this system, and a reduction of finfish effort within the cooperative) or show no consistent change (e.g., mass mortality affecting lobster, for which the cooperative, as for abalone, holds exclusive access rights).Thus, in this system, among the management interventions considered, the ecolabel is expected to have the greatest benefits whereas a reduction in finfishing effort by cooperative members the most detrimental.Moreover, the economic impacts of a mass mortality event of abalones are predicted to be greater than in the case of lobster.
Other studies conducted in this region have documented differential performance of fishers and fisheries in the face of change in environmental conditions.For example, Finkbeiner (2014) found that diversification of fishing activities was important for risk mitigation and stabilizing income, but the ability to specialize on high-value species during favorable conditions resulted in wealth accumulation.Thus, the flexibility to move across fishing strategies given changing environmental conditions is important for the adaptive capacity of small-scale fishing cooperatives.Further research on SES of Baja California and other regions should account for these dynamic responses to change, and how different governance frameworks and markets may enable or constrain adaptation.
Models also highlight what user groups might be more vulnerable to external shocks.In this SES, nonmember income is more sensitive than member income to environmental variability or the management decisions considered in these scenarios (Fig. 4; Appendix 1, Table S2).Interestingly, member income shows resistance to change when the system is perturbed through inputs that affect nonmembers, such as finfish stock, nonmember income, nonmember effort on finfish, nonmember catch, and job opportunities.Should these conclusions survive further scrutiny, they would indicate how management decisions might affect these communities because costs and benefits may be unevenly distributed.This is particularly important as perceived inequity in resource access, illegitimacy of process, and loss of social capital can influence how people comply with regulations, and, if ignored, can lead to unintended consequences, such as increased poaching and declines in species abundance (McClanahan et al. 2009).Ultimately, this can lead to poverty traps and affect the adaptive capacity of SES (Cinner 2011).An important next step will be to conduct in-depth analyses and modeling of social dynamics and possible unintended consequences of interventions in this and other coastal SES (e.g., Finkbeiner 2014).It is important to recognize that governance approaches addressing problems in one SES dimension could trigger unintended consequences in other dimensions if issues are not addressed in the whole system perspective.A comprehensive, integrative understanding of SES in this and other systems will enable sustainability science to more fully inform sustainability practice (Leslie et al. 2015).
Loop analysis can also reveal important potential trade-offs between desirable ecological and social outcomes, and can help identify which interventions may instead lead to potential win-win outcomes.In this case study, for example, management interventions, such as additional finfish fisheries regulation, are expected to have negative economic impacts, whereas creating new jobs through ecotourism or subsidies might have mixed effects on cooperative members versus nonmembers.Market interventions, like the ecolabel, are expected to have overall positive economic effects.Moreover, this positive economic impact is associated with a lack of negative biological impacts under most model structures, indicating that this market-based intervention poses the least trade-offs among those considered.Furthermore, under this scenario, the benefits are distributed across multiple stakeholder groups, in which both members and nonmembers are predicted to thrive.However, we caution applying outcomes from loop analysis without further modeling or empirical support for at least a core set of the variables.For example, our assumption that an ecolabel automatically increases the rate of change of member income may not be applicable in all systems.Although ecolabels can influence market price and increase income, and did result in documented benefits for FEDECOOP cooperative members and nonmembers in this region (Pérez-Ramírez et al 2012b), this is highly dependent on access to markets, infrastructure, and processing capabilities (Pérez-Ramírez et al. 2012a) Loop analysis can identify what pathways may have greater influence on the outcomes, highlighting potentially important relationships to examine in future research and analysis.As described in our results, loop analysis may predict both expected and unexpected outcomes.For example, in this case study loop analysis predicts that an increase of fish stock abundance (FS) has a negative effect on the growth rate of its lobster (LS) but not abalone (AS) prey.As in any network analysis of complex systems, multiple pathways mediate the effects of one variable on another, so the full set of pathways must be examined to understand the effects.In each case (links from FS to LS and from FS to AS), there are multiple pathways carrying opposite effects, i.e., negative and positive.Thus, if only the number of pathways influenced the outcome of the loop analysis, we would expect the results of the simulation to lead to a neutral effect of FS on both AS and LS.Likely this discrepancy between what we would expect based on the number of pathways and what we obtain from the simulations depends on the fact that the product of link values, drawn from a random distribution, can yield small numbers in longer paths whereas the shorter paths tend to drive the final outcome of the loop analysis.In the example discussed above, the shortest paths are both negative from FS to LS but one positive and one negative from FS to AS.
This case study exemplifies the potential of loop analysis in SES applications and highlights the remaining weaknesses and caveats of this approach.In loop analysis, similar to other modeling approaches, predictions are strongly dependent on the specific assumptions about the relevant components of the SES, the nature of the linkages among these components, and the overall structure of the network.A major source of uncertainty is associated with our still limited ability to accurately represent the relationships between the variables.Although our depiction of the socialecological system of the Vizcaino fisheries and decisions about the nature and direction of interactions are based on available knowledge of this and other similar systems, high uncertainty remains.For example, the observed negative impacts on lobster http://www.ecologyandsociety.org/vol22/iss1/art34/stocks that we obtained in several simulations are likely because of the assumption that predation by some finfish taxa (e.g., sheephead, which is targeted by local fisheries) controls lobster stocks.Although sheephead are major predators of lobster and sheephead control of benthic invertebrate populations has been demonstrated in kelp forests of southern California (Cowen 1983), there is no empirical evidence for top-down predatory control of lobster populations along the coast of Baja California.
Increasing the reliability of predictions can be obtained by designing alternative network structures and assessing the robustness of predictions to these different depictions of the linkages.This can help identify which structural differences matter.For example the abalone fishery subsystem (Fig. 3, columns labeled AS, AE, AC) appears to be quite resistant to environmental change.Of the 5 alternative network structures that we analyzed, 22 or more of the 42 predictions related to this subsystem show no response to parameter change (Appendix 1, Table S2).This robust outcome may be the effect of a core structure common to all models upon which few links added or removed do not change the predictions.Thus, it is particularly important that the core structure of models is carefully constructed, integrating all available sources of information and input from different stakeholders.In fact, an important benefit of loop analysis is that it provides a framework for integrating different types of information, thereby offering an opportunity to involve stakeholders in participatory model construction (Anthony et al. 2013).Both for qualitative and quantitative modeling approaches, model development will benefit from implementing participatory frameworks, in which different types of knowledge of the system from different users are included and tested to determine what variables and linkages are most relevant to the outcomes (Essington et al. 2016, Stier et al. 2016).
Our results, besides specific predictions in the different scenarios, highlight that patterns of correlation depend on the network structure and the entry point of the perturbation.For example, abalone (AS) and lobster stocks (LS) are negatively correlated with one another when biological stress enters the system (scenarios 1 and 2).However, when a press perturbation affects nonbiological variables (effort, income, job opportunities, scenarios from 2 to 7), the two stocks appear uncorrelated with one another.It follows that patterns of correlation from field data can be used to detect the entry points of perturbation in the system, and this highlights the potential of loop analysis as a diagnostic tool.
Loop analysis has been used in a few other cases of scenario analysis in the context of fishery (Anthony et al. 2013, Espinoza-Tenorio et al. 2013, Carey et al. 2014, Dambacher et al. 2015).Nevertheless, this technique presents several limitations that must be carefully addressed in management contexts.Justus (2006) outlined what outcomes from loop analysis are with regard to changes in the equilibrium level of the variables, but real systems are generally not at equilibrium, and nonlinearities often characterize variables' dynamics.Although previous studies (Lane and Collins 1985, Bodini 1988, 2000) have offered evidence that loop analysis can be applied to dynamic systems by considering changes in average values of the variables, dynamic changes remain a main challenge for qualitative modeling techniques.Another limitation of loop analysis concerns the time scale at which predicted effects may manifest themselves.For example, change can occur gradually, over long time frames, for some components of SES whereas others may experience sudden shifts.Variables that belong to different domains may show very different dynamics, thus time scales must be carefully considered and directly addressed by combining qualitative analysis and quantitative dynamic models.
Other qualitative modeling approaches can offer some advantages with respect to loop analysis.For example, fuzzy cognitive maps (FCMs) make the magnitude of links explicit through a semiquantification of the relationships between the variables (Özesmi andÖzesmi 2004, Kok 2009).This approach resolves the ambiguities about the net effect of contrasting pathways discussed above.Another advantage of FCM over loop analysis is that it can make predictions about multiple simultaneous perturbations.However, the procedure for constructing FCMs requires experts to describe the structure and the interconnections of the network using fuzzy conditional (IF-THEN) statements.Such statements are of the type "if the level of variable A is high, that of variable B is low."This implies that experts define the relationships from correlations between the variables derived from observing the system (Stylios and Groumpos 1999).Our results highlight that patterns of correlation depend on the network structure and the entry point of the perturbation.For example, abalone (AS) and lobster stocks (LS) are negatively correlated with one another when biological stress enters the system through mass mortalities (scenarios 1 and 2).However, when perturbations affect the system through nonbiological variables (e.g., changes in effort, income, and job opportunities, scenarios 2-7), the two stocks appear uncorrelated with one another.It follows that defining interactions on the base of their correlations may be misleading (Levins and Puccia 1988).
Both loop analysis and FCMs allow for predicting changes in the level of the variables in a complex system following a perturbation to one of them.However, an advantage of loop analysis is that it models the effect of a perturbation to the rate of change of a variable, which isn't dependent on the initial state of the variable.For example, in scenario 1, we investigated the effect of an increased mortality of abalones due to climate change.Although we can expect heat waves and/or hypoxia to increase the mortality of abalone populations, based on available data (Morales-Bojórquez et al. 2008, Micheli et al. 2012), it is more difficult to predict the resulting abundance.In FCMs, instead, the perturbation is simulated as a change in the initial state of one or more variables (i.e., the abundance of a population), but changes in the level of the variables are difficult to predict (Levins and Puccia 1988).Therefore, in our case, loop analysis is more appropriate because it allows the incorporation of disturbances based on the knowledge of the direction of the variables' rates of change (negative, neutral, or positive).Given the strengths and weaknesses of each approach, there is great potential for fruitful integrations as shown by Ramsey and Veltman (2005).
Other qualitative modeling approaches include causal loop diagrams (CLD; Richardson 1986) and Bayesian belief networks (BBN; Borsuk et al. 2004;Pollino et al. 2007).Causal loop diagrams make predictions by logically reconstructing the causal chains of causes and effects between the variables on the basis of link polarities.However, predicting the behavior of complex http://www.ecologyandsociety.org/vol22/iss1/art34/networks, such as the one examined here, by identifying the feedback effects using link polarity is difficult and can lead to misleading interpretations of the effects, as previously highlighted by Richardson (1986).Similarly, specifying the relevant conditional probabilities as required by BBN can be a laborious and time-consuming process (Ticehurst et al. 2007).Moreover, including feedbacks via cyclic network structures requires dynamic time-explicit BBNs that depend on extensive parameterization.Hence, BBNs do not usually include feedbacks common to ecological systems (Marcot et al. 2001).Similar to FCMs, combining BBNs with loop analysis has great potential for improving predictions and model validation (Melbourne-Thomas et al. 2012, Anthony et al. 2013).However it must be emphasized that these applications of BBNs are based on the signs derived from the analysis of the qualitative models.As such, their outcomes are contingent on the assumptions and limitations of the signed diagraph models.

CONCLUSION
Managing fisheries under an ecosystem-based approach requires a shift in focus from single fisheries and sectors to a comprehensive strategy in which management considers multiple fisheries, multiple species, multiple aspects of local communities, and their linkages.Only by taking a holistic view of the SES can we begin to predict the consequences of multiple human activities, management interventions, and environmental shocks.Qualitative modeling approaches allow managers, stakeholders, and scientists to examine which of a suite of possible interventions has the greatest potential to influence other biological and socioeconomic components in the system, and which are more resistant to change.Furthermore, models and their outcomes can help identify key components and linkages, and prioritize data collection and management actions.However, qualitative models including loop analysis are subject to high uncertainty and outcomes of model perturbations are contingent on the assumptions about structural linkages.As such, qualitative models should be tested with empirical data and combined with quantitative dynamic models to increase certainty around model predictions.Despite their limitations, qualitative models that include linkages across the SES are integral to a comprehensive, system-wide approach that addresses ecological integrity, intergenerational opportunities, and economic efficiency, three key dimensions of the sustainable development paradigm.
Responses to this article can be read online at: http://www.ecologyandsociety.org/issues/responses.php/8825

Appendix S-A Loop analysis: making predictions through signed digraphs
In what follows, we are showing how the loop analysis algorithm for predictions works using a simple model.In Figure S1 a simple tri-trophic linear chain comprises a resource (A), an intermediate consumer (B) and a final consumer (C).Loop analysis considers variations in the level of the variables as consequences of perturbations that permanently alter the rate of change of the variable.Suppose that c is the mortality of species A. If c is reduced (e.g. because of improved environmental conditions, or the establishment of a marine reserve), then the rate of change for A is expected to increase.We call this a "positive input".It is formally represented in Figure S1 as the derivative of the growth function for A (  in respect to the variation ofc  .Because parameters in the equations for the growth rate of variables (i.e.  =  , , , , , … in which , ,  are parameters) define the equilibrium points for the system, changes in parameter values define new equilibrium points with new values for the level of the variables.This parameter variation may influence the abundance of all variables in the model.Loop analysis algorithms predict the direction (increase, decrease, no variation) of change for the level of the variables.
The loop analysis algorithm and its structural elements, with examples of calculations, are visually represented in Figure S1.
The following formula summarizes the elements of the algorithm: Besides the sign of the input, determined by the term !" !!" , the loop formula makes use of the concepts of path, circuit, complementary feedback, and overall feedback.These refer to structural elements that can be identified in any graph.Their meaning can be fully understood by referring to the correspondence between matrix algebra and the formalism of loop analysis (see Levins 1975, Puccia andLevins 1985).In the above formula, c is the changing parameter (e.g., mortality, fecundity, predation rate);  ! designates if the growth rate of the  − ℎ variable is increasing + or decreasing − ; [ !" (!) ] is the pathway connecting the variable that undergoes parameter change,  !, with that whose equilibrium value is being calculated,  !, and that includes  variables.The last factor of the numerator is the complementary feedback [ !!! (!"#$) ], which buffers or reverses the effect of the pathway; it is the feedback formed by the  −  variables that remain in the system after the  variables that are on the path are excluded.The term [ !] indicates the overall feedback of the system, which is a measure of the inertia of the systems to change.Criteria to identify such elements in the example graph are provided by using the scheme depicted in Figure S1 Figure S1.Signed-digraph of a three trophic level linear chain.Paths, complementary subsystems, and feedbacks used to calculate expected changes in the equilibrium level of the variables, in response to a positive input on A. The first term of the numerator in the formula under the Prediction header is the sign of the input (+).

Circuits and Feedbacks.
In loop analysis, a pathway that starts at one node and, by following the direction of links, returns to it without crossing intermediate nodes more than once is called a loop, or circuit.Any circuit produces a feedback that can be either positive or negative, depending on the product of the signs of the links that form the loop.As there may be circuits of different length (with 1, 2, 3, ..., k variables involved), in a given system there are as many levels of feedback as variables.Each level of feedback considers all the circuits (feedbacks) involving that particular number of variables.In the system of Figure S1 there are 3 levels of feedback.The first level of feedback comprises the only one variable circuit that is present in the system: the self-damping on variable A. Two resource-consumer interactions o →  and o →  produce two feedbacks of the second level, and the three variable feedback shown in Figure S1 (overall feedback) form the third level of feedback, which is created by two independent loops: the selfdamping on variable A and the resource consumer interaction involving B and C.
Overall Feedback (F n ).The overall feedback is computed only once and corresponds to the highest possible level of feedback in a system.It can be calculated from single circuits linking all the variables in the system, or as a combination of shorter circuits involving smaller subsets of variables.In the hypothetical chain of three trophic levels depicted in Figure S1, the overall feedback corresponds to a third level of feedback (that is a feedback effect involving all three variables).Because the three variables cannot be connected simultaneously in unique circuits, the overall feedback comprises all the products of disjunct loops that have a combined number of variables equal to 3. That is, F n is composed by the self-damping on A (a self-effect link is a loop of length 1) plus the two-node loop [B-C].Its sign is obtained by multiplying the signs of the links involved, and this sign is further multiplied by −1 !!! , where m is the number of disjunct loops entering the feedback.As the links involved are two negative and one positive, and there are two disjunct loops, the overall feedback is negative. (!) ].A path is a series of links starting at one node and ending on another node, without crossing any variable twice.Suppose a positive input occurs on A (its rate of change increases, !" !!" > 0).To predict the new equilibrium of C, the path along which the effect travels is the positive link from A to B and the arrow from B to C. Its sign, given by the product of the signs of the links that form the path, is positive.

Complementary Feedback (F n-k
).The complementary feedback is the feedback that groups all the variables in the complementary subsystem.The complementary subsystem is what remains after the  variables in the path are excluded.In Figure 1, for a positive input on A and effect on B, the complementary subsystem is formed only by C (A and B are on the path).Because C has no self-effect link, in this example there will be a null (0) complementary feedback.A path from a variable to itself is equal to 1, while if all the variables are in the path (i.e., input to A and effect on C) there is no complementary subsystem, and the complementary feedback is equal to -1.These are two algebraic conveniences that are formally explained in Levins (1975) and Puccia and Levins (1986).Summation in the loop formula considers the fact that two variables can be connected by more than one path.
Using linear algebra, we obtain the same prediction as the graphic algorithm and the net effect (the sum of the direct effect plus all the individual indirect effects) on species i resulting from an input on species j is given by the element of the inverse community matrix: For simplicity, the vector is considered equal to one because there is no quantitative information about the inputs.A summary table of predictions can be produced from the simulated matrices that satisfy stability conditions.In the overall table, the variables' response is quantified as the percentage of positive signs, negative signs and zero values obtained from the matrices.The sign of the prediction is determined by a set of rules regarding the percentages of cases in which +, -and 0 appear in any given entry of the table, as we explained in the main body of the paper.
Table S3.Sensitivity Analyses.Number of cases in which each prediction matrix differs from all other matrices in a series of pairwise comparisons.a. Numbers based on tendencies of changes (i.e.including ?+ and ?).The greatest difference is between models 2 (M2) and 3 (M3) (55 cases, corresponding to 28% of the total number of comparisons).The average difference computed considering all comparisons is 20%.S3a) when tendencies are transformed in signs (i.e.?+ becomes + and ?-becomes -).The largest difference is between models 2 and 3 (35 cases): their predictions differ in 17% of the comparisons.The average difference is 12%.S4.Control over lobster effort through regulation.In this model, control is exerted by a governmental agency (GA) that is represented in the graph as a "predator" on LE (lobster fishing effort).This represents the situation where a controlling factor (GA, in this case) reacts promptly to any variation in the level of effort, bringing it back to its original level.This controll is possible because of the negative feedback between GA and LE and because GA is not self-damped.Without self-damping, GA responds only to LE.Its response is typical of a negative feedback that exerts a buffering effect.Moreover, LE remains unaffected by any input entering the system because GA, being non self-damped, makes the complementary feedback of all pathways to LE null.Therefore, GA protects LE against the effect of variations in the system.The table of predictions is reported below.The table shows that LE changes only for variations in the rate of change of the governmental agency which controls it.

Figure S1
. Control over lobster effort through regulation (see Table S4).

Fig. 2 .
Fig. 2. Signed-digraph representation of the social-ecological system (SES) interactions in the Baja California fisheries case study.Variables are : MI (cooperative member income); JO (job opportunities for nonmembers); NI (nonmember income); ME (members effort on finfish); NE (nonmembers effort on finfish); MC (finfish catch by members); NC (finfish catch by nonmembers); FS (finfish stock); LE (lobster effort, by members only); LC (lobster catch); LS (lobster stock); AE (abalone effort, by members only); AC (abalone catch); and AS (abalone stock).Arrows represent positive interactions, where a variable leads to a positive rate of change in the other, and lines with open circles represent negative interactions, where a variable inhibits the rate of change in the other.The main model (model 1) includes predator-prey relationships among the three stocks, abalone, lobster, and finfish, and negative relationships among fishing effort between the abalone and lobster fisheries and the lobster and finfish fisheries.The other four model structures are variations on this primary model and remove some of the linkages among fishing efforts (models 2-5).

Fig. 3 .
Fig. 3. Tableillustratingexpected directional changes in the levels of the components of model 1 (Fig.2).Alteration in the rate of change of any row variable results in expected variations in the level of the column variables.Green arrows indicate a positive change (75-100% of the linkages from the model runs were positive), whereas green triangles indicate a tendency toward a positive change (60-75% of the linkages were positive).Red arrows indicate a negative change (0-25% of the linkages from the model runs were positive), while red triangles indicate a tendency toward negative change (25-40% of the linkages were positive).Zeros (yellow dots) reflect compensation between positive and negative effects that result from the model runs and likely no change would be expected in the variable's level.Predictions are obtained by assuming positive inputs (i.e., increased rates of change of the variables) to the row variables.Predictions for negative inputs (decreased rates) can be easily obtained by simply inverting the direction of the arrows and of the triangles (and the colors).The first letter of the variable labels (in the rows and columns) identifies a system component (e.g., A for abalone, L for lobster, F for finfish), the second letter a specific descriptor of that component (e.g., S for stock size, E for effort, C for catch; see Figure2legend for a complete list of the variables and their acronyms).

Fig. 4 .
Fig. 4. Results from loop analysis examining the effects of external drivers and management decisions from a suite of proposed scenarios, including: (1) increased abalone mortality caused by disease or climate change; (2) declines in lobster stocks from disease or hypoxia; (3) increases in member income from implementation of Marine Stewardship Council (MSC) certification; (4) nonmember income increase through external opportunities (e.g., price increase); (5) management decision that leads to decrease in member finfish effort; (6) management decision that leads to decrease in nonmember finfish effort; and, (7) increase in job opportunities (e.g., from subsidies).Outcomes for each variable from each scenario are given for the main model (Model 1, Fig.2), which includes all linkages of the social-ecological system.Bar graphs indicate the percentage of positive outcomes from the loop analysis model runs.
This means that  !must have a non-zero determinant and must admit an inverse matrix  !!! whose eigenvalues have to satisfy the Lyapunov condition of stability.