Research

INTRODUCTION

Polycentric governance systems feature policy actors operating at multiple levels of geographic scale. Gibson et al. (2000:219) defined scale as “the spatial, temporal, and quantitative, or analytical dimensions used by scientists to measure and study objects and process.” In the context of social-ecological systems, Cash et al. (2006) described various levels of geographic scale, including patches, landscapes, regions, the globe. The effective governance of social-ecological systems requires building policy networks that support bonding and bridging social capital (Berardo and Scholz 2010, Bodin et al. 2017). Bonding social capital facilitates cooperation and learning for collective-action problems as policy actors engage in redundant and recurrent interactions. Bridging social capital facilitates information diffusion and policy learning across boundaries. As a specific type of bridging social capital, cross-scale networks facilitate resource exchange when actors at one level of geographic scale have resources needed by actors operating at a different level (Cash et al. 2006, Lubell 2013, Guerrero et al. 2015a, McAllister et al. 2015a, Sayles and Baggio 2017). Taken together, polycentric governance is more effective when policy actors develop networks that align with the spatial structure of the involved collective-action problems.

Given the multi-level structure of polycentric systems, we examine the argument that policy networks are “scale dependent” in both structure and function. Drawing from ecological studies, scale dependency indicates that patterns and processes observed at one scale may manifest distinct characteristics when examined at other scales of analysis (Levin 1992, Poteete 2017). For example, cross-national studies have indicated that exposure to extreme weather events does not lead to an increase in national policy efforts aimed at strengthening adaptive capacities; however, it has been observed that individual citizens tend to manifest greater support for adaptation policies following their personal experiences with extreme weather events (Ray et al. 2017, Nohrstedt et al. 2021). The drivers of ecological and social patterns can exhibit variability across levels of scale, primarily due to the presence of heterogeneity and variance in social-ecological parameters at lower levels of geographic scale that become more homogeneous as the analysis progresses to higher levels (Levin 1992, Gibson et al. 2000). Failure to consider scale dependency can result in policy responses that are inadequate in addressing cascading or knock-on effects that occur across different levels of scale (Cash and Moser 2000). This oversight has the capacity to worsen social inequities because it might lead to the erroneous identification of focal points of vulnerability and marginalized populations (Hinojos et al 2023).

To study scale dependency, we adopted the approach proposed by Gibson et al. (2000) to analyze policy networks as a series of nested entities at different levels of geographic scale. We constructed local policy networks consisting of policy actors operating at a limited geographic extent, then added subregional actors operating at a broader level, then finally regional actors operating at the full extent of our study area. This allowed us to study how the structure of policy networks varies across levels of geographic scale, and whether the same hypothesized drivers of network formation are correlated with network structure at different levels. As the policy networks expand to involve actors at higher levels, the resulting structural changes are influenced by the constraints and opportunities at those higher levels as well as their interactions with heterogenous local conditions (O’Neill et al. 1989, Gibson et al. 2000).

Based on this approach, we developed two hypotheses about scale dependency in policy networks in the context of the rapidly growing and changing polycentric governance system for climate and sea-level rise (SLR) adaptation in San Francisco Bay (SF Bay), California (Lubell and Robbins 2021). First, we hypothesized that the structure of policy networks varies across levels of geographic scale, and regional-level networks have more structural features that support learning and cooperation. Compared to local actors, regional actors, especially state government agencies, have greater resources and authority to build network structures that enable cooperation and learning (Ingold and Fischer 2014, Angst et al. 2018, Lubell and Robbins 2021). Regional actors also have decision-making jurisdictions that span across geographic and political boundaries, along with organizational goals to build collaboration.

Second, we hypothesized that how policy networks respond to problem severity depends on geographic scale, with local-level networks being more responsive than regional-level networks. Collective-action problems pose risks of undesirable social outcomes that policy actors often experience as “problems” or “issues.” Local networks are more sensitive to these risks due to the spatial variability typically observed at the local level and transaction costs associated with heterogeneous local contexts (Bodin and Crona 2009). Sea-level rise is heterogenous at the local level, and the net benefits for forming policy networks are greater for local communities that are more vulnerable. In contrast, policy actors operating at higher levels of geographic scale are concerned about the entire region and distribute policy resources across different types of local actors. Although local actors may only consider their local risks, regional actors must consider infrastructure or ecological processes that cascade across regions (Lubell et al. 2021). Hence, we expect a weaker association between the level of SLR vulnerability and network configurations of regional-level networks.

We relied on a stakeholder survey to define networks at multiple levels of geographic scale based on the number of local coastal planning units in which policy actors engage. Policy actors range from local to regional and include governmental and non-governmental organizations. Social network and regression analysis demonstrate that regional actors are a crucial source of social capital for solving climate adaptation collective-action problems, and that sea-level rise vulnerability is especially associated with the emergence of bonding social capital.

THEORETICAL BACKGROUND: SCALE DEPENDENCY IN POLICY NETWORKS

We reviewed the existing environmental policy network literature to establish the theoretical and empirical basis for our core hypotheses. A basic assumption of the policy network literature is that policy actors select partners in which the network benefits outweigh transaction costs of searching, bargaining, monitoring, and enforcing collaborative relationships (Jones et al. 1997, Robins et al. 2011, Lubell 2013, Berardo and Lubell 2019). Policy networks help actors address collective-action problems. However, actors with fewer political and material resources are less likely to overcome transaction costs. In multi-level, polycentric systems, policy actors consider the benefits of developing bonding, bridging, and cross-scale networks that shape the relationship between local and regional actors and enable learning and cooperation within and across levels of geographic scale (Vantaggiato and Lubell 2022).

Social capital and geographic scale

Policy network research draws on the concept of social capital to argue that different kinds of network structures enable processes of learning, coordination, and cooperation (McAllister et al. 2015b, Bodin et al. 2017, Mewhirter and Berardo 2019). Both the general social network (Granovetter 1973, Burt 2004) and the policy network literature (Berardo and Scholz 2010, Aldrich and Meyer 2014) make a distinction between bridging and bonding social capital. Although conceptualizations of bonding and bridging social capital could lie in social identity (Aldrich and Meyer 2014), we follow Burt’s (2005) argument that social structures are indicative of social capital. Bonding social capital is provided by “closed” networks with redundant and clustered ties, which facilitate cooperation, trust, reputation, and social sanctioning. Bridging social capital is supported by “open” network structures that span boundaries and structural holes, and thus facilitate information diffusion and learning. Cross-scale networks supply an important type of bridging to social capital in polycentric systems because they facilitate resource exchange and learning across levels of geographic scale. The transaction cost interpretation is that open networks are more efficient for solving information and coordination problems, whereas the free-riding incentives of cooperation problems require incurring the additional transaction costs of redundant ties.

However, both benefits and transaction costs may vary according to levels of geographic scale (Prager 2010, Hamilton and Lubell 2018) and according to whether actors are forming cross-scale networks (Ramirez-Sanchez and Pinkerton 2009, Guerrero et al. 2015b, Kalesnikaite and Neshkova 2021). Alexander et al. (2017) suggested that changing ecological conditions in one marine protected area catalyzes policy learning and cooperation among local actors, while cross-scale ties among local and regional actors emerge in response to the same threats to ecologically connected areas. In the context of wildfires in Sweden, Norhstedt and Bodin (2020) suggested that policy integration is a catalyst for the formation of local networks linked by cross-scale ties to central regional hubs. Cross-scale networks supported by a few central actors can enhance the flow of information and reduce transaction costs for actors facing common problems (Barnes et al. 2017). The combination of clustered local networks with cross-level ties confers “small world” properties that facilitate both information flow and cooperation (Hileman and Lubell 2018). Lubell and Robbins (2021) demonstrated that as the polycentric governance system for sea-level rise adaptation in SF Bay has evolved over time, it has experienced a decentralization process whereby regional actors have transferred resources to local policy forums.

We build on this literature by arguing that as policy networks increase in levels of geographic scale, they are more likely to feature structures that support both bridging and bonding social capital. This argument considers the distinct incentives and capacities of regional and local-scale actors. Local policy actors, such as municipal governments and local community groups, exhibit greater heterogeneity in terms of problem severity and available resources to overcome transaction costs, such as financial resources, expertise, and political authority (Kim et al. 2022). On average, local actors have fewer resources overall than regional actors, such as regional planning entities or state governments. Consequently, local actors often face a trade-off between establishing bridging and bonding ties, with bridging ties being preferable due to their ease of establishment and lower commitment requirements for maintaining collaborative relationships (Ingold et al. 2021). Moreover, the acquisition of in-depth knowledge about local politics and environments by local actors can increase the transaction costs associated with initiating collaboration because place-based specific knowledge may not easily transfer across different local communities (Coggan et al. 2010). Additionally, local actors specializing in specific aspects of social-ecological systems may be unwilling or incapable of integrating diverse knowledge and adopting a holistic perspective (Angst et al. 2018). In contrast, regional actors have greater access to policy resources and their mission includes facilitating regional learning and cooperation to address collective challenges, such as sea-level rise (Angst and Brandenberger 2021). Thus, we expect local networks will have smaller sizes and fewer structures related to bridging and bonding social capital.

We also expect local networks to be geographically heterogeneous, with some local jurisdictions building strong networks in response to a problem while others are left behind. Local jurisdictions that are less capable of building networks bring up questions of equity and environmental justice. Disadvantaged local communities, constrained by deficits in financial, human, and political resources, are less likely to be formally represented in collaborative governance (Dobbin and Lubell 2021). Even governance arrangements that seek to be inclusive may fail to empower disadvantaged local communities when those communities do not have the capacity and resources to participate (Paloniemi et al. 2015). As the networks scale to the regional level, the inclusion of actors with a broader mission and more resources will create larger networks in which bridging and bonding social capital co-exist. The co-existence of bridging and bonding social capital is observed in core-periphery networks where regional actors develop relationships among multiple local jurisdictions (Borgatti and Everett 2000, Vantaggiato and Lubell 2022).

Hypothesis 1: Relative to local policy networks, regional policy networks will include more structures that support bridging and bonding social capital.

Problem severity and geographic scale

A basic assumption of the environmental policy literature is that the benefits of forming policy networks are positively correlated with problem severity, i.e., the severity of the risks actors will experience if they fail to solve the problem. The general expectation is that severe problems catalyze network formation (Dinar et al. 2011, Hamilton et al. 2019, Nohrstedt and Bodin 2020). This goes back to Ostrom’s (1990) observation that degraded common-pool resources stimulate local governance, and Kingdon’s (1984) argument that focusing events catalyze policy change. Numerous studies across diverse environmental contexts, including climate risks, support this general proposition (Bodin and Crona 2009, Hicklin et al. 2009, McGuire and Silvia 2010, Hamilton et al. 2019, Parker et al. 2020).

We extended this literature by arguing that responsiveness to problem severity is scale dependent, where the correlation between natural hazard exposure and network structures varies depending on the selection of analytical scale (Hinojos et al. 2023). By responsiveness, we mean that as vulnerability to sea-level rise increases at the local level, there are increasing benefits to developing network structures associated with bonding and bridging social capital. For bonding social capital, the benefits derive from creating network structures that facilitate cooperation among local actors facing a common climate risk (Coggan et al. 2010, Barnes et al. 2017). For bridging social capital, the benefits derive from accessing information, funding, authority, and other policy resources from other policy actors at the same or different levels of geographic scale (Coggan et. al 2010, Kalesnikaite and Neshkova 2021). At the local level, there is spatial heterogeneity in the distribution of problem severity, and the benefits of network formation outweigh the costs only when the problem is salient (Paavola and Adger 2005, Fried et al. 2022). Hence, the local-level variance in SLR risk will exhibit a positive correlation with bonding and bridging social capital. Specifically, we expect local networks in more vulnerable geographies to have a higher average degree, more centralization, more transitivity, and more cross-level ties.

In contrast, regional level actors, such as regional planning entities or state governments, are more likely to consider interdependencies that emerge from cascading processes and create regional collective-action problems. For example, when one local community builds a seawall, they may influence hydrodynamic processes and increase or decrease flood risk for other communities (Wang et al. 2018). Regional level actors often actively engage or even create policy forums that prioritize regional environmental problems, leading them to promote the integration of diverse knowledge and resources across the region (Angst et al. 2018, Hamilton and Lubell 2018). Regional actors possess better information and demonstrate greater concern for the fact that actions taken by local actors can have wide-ranging impacts on the benefits and costs for other actors. Furthermore, the information and other policy resources provided by regional actors have public good characteristics available to all stakeholders and thus help meet distributive political goals. In contrast to local actors, regional actors may invest in networks even in local jurisdictions that are not directly experiencing the problem. Hence, regional networks experience a smoothing effect, reflective of broad responsiveness to problem severity throughout the entire Bay area, rather than being confined to localized SLR vulnerability. Analogous to how ecologists think about scale dependency, local actors respond to variance across geography, whereas regional actors respond to common problems within their territory. Hence, we expect regional policy networks to be less correlated with local spatial heterogeneity in problem severity.

Hypothesis 2: Local policy networks are more strongly correlated than regional policy networks to local spatial heterogeneity of problem severity.

METHOD

Survey and data collection

Our research design comprises key informant interviews, participant observation of policy meetings, and a web-based survey. We conducted semi-structured interviews with 39 key informants directly involved in sea-level rise adaptation (see Appendix 1) and thus created a seed list of contacts comprising 800 individuals, representing 309 organizations. Further, we mined the contact lists of the key policy forums concerning SLR that were taking place across the Bay area, to obtain a large list comprising 3087 individuals representing 623 organizations. We invited all individuals in our contact list to complete a survey on June 25th, 2018. Our sampling frame was purposely inclusive because it was impossible to determine whether individuals and organizations were actively involved in the governance system or just casual observers. We also asked our survey respondents to invite individuals that they know deal with sea-level rise in the Bay area to obtain a personalized survey link from us. We received 18 requests for survey links. We closed the survey on September 10th, 2018. We had a response rate of 22% in terms of individuals, for a total 722 respondents.

To measure policy networks, the survey asked respondents to list the federal, state, regional, local, and non-governmental actors they collaborated with for issues related to sea-level rise in the SF Bay area in the previous year. In a separate question, the survey provided respondents with a map of the Bay area subdivided into 30 shoreline segments, called operational landscape units (OLUs), and asked them to click on the ones they focus on for SLR. That is, the linkage between policy actors and OLUs is a binary variable that can only measure whether policy actors engage in OLUs, rather than the extent of policy engagement. The OLU framework, developed by the San Francisco Estuary Institute (SFEI), divides the Bay shoreline into 30 distinct geographic areas that share common physical characteristics but cross the traditional jurisdictional boundaries of cities and counties. Operational landscape units encompass the entire Bay shoreline and cover the region’s land area potentially vulnerable to future sea-level rise (https://www.sfei.org/adaptationatlas). Key state and regional agencies have adopted OLUs as an important geographic unit for sea-level rise adaptation planning.

To construct policy networks for individual OLUs, we used our respondents’ self-reported collaborative ties and OLUs where they engaged in the governance of SLR. Of 722 respondents, 443 listed the organizations they have collaborated most closely with in the context of sea-level rise planning during the past year, representing 297 organizations (network nominators). They nominated an additional 321 organizations (network nominees), including survey non-respondents and survey respondents who do not report collaborative relationships. Altogether, there are 618 unique organizations identified within the boundaries of the collaboration network. In our study, 299 organizations provided self-reported information regarding the OLUs they are actively engaged in. To account for the missing information on self-reported OLU engagement for 319 organizations, we followed an approach employed in prior literature by supplementing the data with objective information (e.g., Guerrero 2015b, Alexander et al. 2017, Di Gregorio et al. 2019, Jasny et al. 2019). Specifically, for governmental agencies, we considered the number of OLUs covered by their administrative jurisdictions. For non-governmental agencies, we used the OLU engagement of their collaborators as a proxy measure. Appendix 7 compares actors with the self-reported and supplemented OLU information and finds some significant differences between them only in the case of state and federal actors, whose regional outlook (i.e., connections to all 30 OLUs) might be overestimated based on the supplemental information. We discuss the potential implications of this overestimation in the appendix.

Network analysis

We constructed policy subnetworks at distinctive geographic scales for each OLU. First, for all policy actors (both governmental and non-governmental) directly associated with a focal OLU, we classified their levels of geographic scale as local, subregional, or regional. Local actors are those who work on one to seven OLUs, including the focal OLU. Subregional actors work on 8 to 20 OLUs, and regional actors on more than 20 OLUs. We chose these breaks to classify policy actors for two main reasons. First, in four OLUs (Carquinez North, Carquinez South, Port Chicago, and San Lorenzo), there are no ties between actors who engage in five or fewer OLUs. Given our limited sample size (30 OLU), we decided to set the break for local actors at least larger than 5 OLUs.

Second, we picked seven OLUs as the upper boundary for local actors based on the subregion defined in the Bayland Ecosystem Habitat Goals Update, also known as Goals Project 2015 (Goals Project 2015). The main purpose of the Goals Project, a collaboration among scientists and managers from various organizations, is to provide recommendations on restoration goals for ecological needs in the Bay area. It defined 20 segments to capture the basic ecological and geomorphic units of the Baylands and 4 subregional areas: Suisun, North Bay, Central Bay, and South Bay. We believe that this piece of information could provide hints on how policy actors define subregional areas. Hence, we matched OLUs and subregional areas of the Goal Project according to the Bay Shoreline Adaption Atlas published by San Francisco Estuary Institute (SFEI). The average number of OLUs in one subregional area is 7.5. Therefore, we define local actors as engaging in 1-7 OLUs. We expect regional actors engage in more than three subregions, so 20 OLUs is selected as the break between subregional and regional actors. Among 610 organizations, there are 375 local actors (61.48%), 46 subregional actors (7.54%), and 189 regional actors (30.98%; see Fig. 1 for the distribution of the number of OLUs where policy actors engage). We are aware that these breaks may be arbitrary and could potentially affect the results. Additional analyses by defining policy actors with varying numbers of OLUs that they engage with are conducted. The general pattern remains consistent (see Appendix 3).

The unit of observation is 30 OLUs. We sliced the whole policy network for the focal OLUs into three subnetworks by geographic scales of policy actors and calculated network statistics. Local networks would only include local actors. Subregional networks incorporate subregional actors into local networks. Regional networks would have all policy actors at various geographic scales in the focal OLU. Sociograms of policy network for each OLU across geographic scales can be found in Appendix 2. This approach allowed us to observe the nested structure of policy networks and assess how network configurations change from lower to higher levels of geographic scale.

As shown in Figure 2, we used network size (number of nodes), density (ratio of observed to possible ties), and average degree (the average number of edges across nodes) to describe policy actors and their connectivity in subnetworks at different levels of geographic scale. To test hypothesis 1, we calculated measures of global network structure related to bridging and bonding social capital. For bonding social capital, we calculated transitivity, triangle percentage, and modularity. Transitivity measures the tendency for networks to cluster, when actor i is connected to actor j, and actor j is connected to actor k, then actor i would be connected to k. Transitivity enables “friends of friends” processes or closed networks that facilitate cooperation. Modularity measures the extent to which the network is broken up into sub-communities by taking a random walk approach (Pons and Latapy 2006). High modularity indicates the network’s ability to partition into isolated sub-communities wherein community members are densely connected (Newman 2006). This fragmented network structure implies the prevalence of bonding ties within cohesive subgroups, while the existence of bridging ties across the entire network is relatively limited (Bodin and Crona 2009, Norbutas and Corten 2018).

For bridging social capital, degree centralization measures the extent to which a network is organized around one or more central actors who have higher connectivity with others; betweenness centralization measures the extent to which a network is organized around one or more central actors who connect actors that would be disconnected otherwise. Centralized networks have more open structures in which redundant ties among nodes are relatively rare.

We also calculated two measures of cross-scale policy network relationships: average short path across scales and cross-scale network density. Average short path across scales is calculated by taking the mean of the shortest path between pairs of nodes across levels of geographic scale in regional networks with multilevel actors (Bianconi 2018). A smaller value represents that on average, nodes at the lower level can directly reach out to ones at the higher level. Cross-scale network density is a ratio of observed cross-level ties into the maximum number of possible cross-level ties for a multilevel network. Mathematically, it would be the number of observed cross-level ties divided by the product of the numbers of nodes at the lower and higher levels. These cross-scale linkages are expected to offer opportunities for the transfer of diverse knowledge and resources by connecting actors at one level of geographic scales to others at different levels (Carlsson and Sandstrom 2008). As actors establish more connections across various hierarchical levels, their potential to access information and resources beyond their geographic boundaries can expand. However, it is crucial to acknowledge that excessive cross-scale linkages may inadvertently result in redundancy of information and resources (Bodin and Crona 2009, Sayles and Baggio 2017). Using cross-scale density allows us to capture and assess the overall pattern and prevalence of bridging connections among actors across geographical levels.

To complete the test of hypothesis 1, we used conditional uniform graph (CUG) tests (Butts 2011) to assess whether network statistics observed in the subnetworks are more or less frequent than would be expected in a distribution of simulated random networks. To account for the potential confounding effect of other network features, we simulated random networks that match the size and density of the observed networks. Following Levy et al. (2018), we calculated the network statistics for 10,000 simulated networks to form statistical distributions. We then calculated t-scores by taking the difference between the observed values and the mean of the simulated distributions divided by the standard deviation of the simulated distributions. A higher t-score means the observed network has a higher abundance of a structural feature than would be expected at random, while lower t-scores indicate a dearth of such structures.

To test hypothesis 2, we estimated OLS regression models in which problem severity is a key explanatory variable to correlate with network statistics across geographic scales. We measured problem severity using data from the US Geological Survey coastal storm modeling system and calculated the percentage of land area in each OLU forecast to be inundated during a 100-year storm event under a 25-centimeter sea-level rise scenario. As control variables, we included population density and the number of resilience projects reported in the San Francisco Bay Regional Coastal Hazard Adaptation Resilience Group (CHARG). Population density is a proxy for economic damages that might occur from flooding. The number of resilience projects in an OLU is an indicator of adaptation activities that are supported by networks. The regression models also control for network size, which is strongly associated with many types of network properties. Appendices 4 and 5 report sensitivity tests that control for past storm events and spatial autocorrelation.

RESULTS

Regional networks have more social capital

To provide a sense of the empirical patterns, Figure 3 visualizes policy networks from three illustrative OLUs. The networks suggest interesting patterns across levels of geographic scale within each OLU, as well as between OLUs. At the local and subregional scales, the networks are sparser with some especially active nodes serving as hubs for a larger core community, with a periphery of disconnected actors. But the networks undergo a “phase transition” of sorts once the regional actors are connected to the OLU: they become larger, denser, more centralized, and more connected. Concurrently, across OLUs, the local and subregional networks are more heterogeneous. For example, the Wildcat OLU has a very sparse network, while the Belmont-Redwood network has at least one active community, and the Mission-Islais network has a broader set of connections across multiple hubs. In contrast, the regional networks aligned with each OLU are more homogenous because most regional actors have overlapping connections to multiple OLUs. The homogeneity and overlapping connections of regional actors is a fundamental feature of regional, polycentric governance systems in which regional actors are concerned with distributing policy resources to influence local decisions (Gerber and Gibson 2009).

The CUG tests evaluate the statistical importance of the observed networks, relative to a random distribution of networks of the same size and density. Average degree is not included in the CUG tests because it is a function of network size and density. Violin plots present the t-score distribution of network measures for 30 OLUs policy networks at different levels of geographic scale. Specifically, the width of the violin plots indicates the frequency of t-score for OLUs. The marker in the box plot shows the median of the t-score distribution.

Consistent with hypothesis 1, Figure 4 shows that for all network statistics, the local and subregional networks have more variance while the regional networks are far more homogenous. The regional networks are much larger on average and show the usual pattern of lower density for larger networks. Concurrently, the regional networks have a higher average degree (more connectivity, controlling for size) and lower modularity. The local and subregional networks have a bi-modal distribution of average degree, suggesting that some local networks are better connected than others. The regional networks also have much higher transitivity and completed triangles, which indicates cooperation structures around a central core. The lower-level networks tend to be more fragmented into multiple disconnected communities, which in some cases (see Fig. 4) may include a small active group surrounded by an inactive, disconnected periphery. The higher levels of centralization for the regional networks also support the idea of a core regional network that involves structures for both learning and cooperation.

Figure 5 confirms that regional networks have much higher levels of transitivity and centralization than lower-level networks. Regional networks are also less modular, i.e., not as fragmented into multiple communities as some local networks. Moreover, the regional network measures are consistently different than what would be expected from the distribution of simulated networks of the same size and density. For example, the median of the t-score distribution of degree centralization in regional networks for all 30 OLUs is around 47.17, far from zero, indicating that the difference between the observed degree centralization and the degree centralization of the simulated random networks is statistically significant. That is, for all OLUs, the regional network tends to be organized around one or more central actors who have the most connectivity. In contrast, the t-score of degree centralization in the local and subregional networks varies across OLUs. For some OLUs, the t-scores of degree centralization in the local and subregional networks are closer to zero. On the contrary, other OLUs have t-scores much higher than zero. Taken together, the variance of the t-score of degree centralization in the local and subregional networks for each OLU illustrates heterogeneity of local and subregional policy response to the threat of sea-level rise.

When it comes to cross-level connectivity (see Fig. 5c), the cross-scale relationships have a higher average path length and lower density than expected in random networks, which suggests there are barriers to forming cross-level relationships. The average path length for local-regional ties is slightly higher than other cross-level ties (albeit not statistically significant; Fig. 5c), and the density of local-regional ties is the lowest. Although the lower density of local-regional ties might be partially due to the smaller number of subregional actors; the higher average path length suggests that the transaction costs of cross-scale ties increase as a function of the distance between levels of geographic scale.

Local networks are more responsive to problem severity

Tables 1-3 report the regression results in which local sea-level rise vulnerability is the key predictor variable associated with network structures at different levels of geographic scale. For bridging social capital, there is no evidence that problem severity is associated with centralized networks (i.e., open structures; see Table 1). These patterns remain consistent when we treat the geographic scope of policy actors as a continuous variable (see Appendix 3).

The results for bonding social capital show some evidence of scale dependence (Table 2). Transitivity is positively associated with local sea-level rise vulnerability across all scales, but the correlations are stronger at the local and subregional scale and weaker at the regional scale. This suggests lower levels of geographic scale respond to problem severity by building network structures that facilitate cooperation. Concurrently, sea-level rise vulnerability is associated with less modular and fragmented networks at the subregional level, which suggests the subregional level is a crucial transition into a more core-periphery structure.

In our data structure, neighboring OLUs could have shared policy actors and then similar network structures. To account for the potential influence from neighborhood OLUs, we first counted the number of shared policy actors between adjacent OLUs and included this variable into the regression models. As shown in Figure 6, the pattern remains consistent. Although problem severity is not associated with centralized networks, it is positively associated with transitivity and triangle percentage. It is also important to note that the size of SLR coefficients shrinks as policy networks scale up from local to regional levels. Additionally, we conducted an additional test to explicitly account for network autocorrelation, and the results obtained from this test align with the findings here (see Appendix 6).

Moreover, exposure to common environmental challenges, frequent social interactions across nearby locations (i.e., local spillover), or both, could produce specific spatial patterns of policy networks, although we are unsure about which mechanisms are at play. Thus, we ran a series of tests and employed spatial regression models to control spatial contagion by including spatially lagged dependent variables from neighbors (see Appendix 5). Interestingly, the results indicate that bonding network structures at the local and subregional level would be associated with neighborhood effects from immediate neighbors because the spatial lagged variable is statistically significant whereas sea-level rise vulnerability is not significant. As the definition of nearest distance expands to include more neighbors, the spatial neighborhood effect is no longer significant, while sea-level rise vulnerability becomes a significant predictor (Appendix 5, Tables A5.8-A5.12). On the other hand, for regional-level networks, the coefficient for SLR vulnerability is significant even with spatial autocorrelation (Appendix 5, Tables A5.10, A5.13). These findings suggest that the presence of local network externalities could potentially diminish the association between problem severity and local policy networks, and this impact would hinge on the spatial definition of the sources from which local network externalities emanate.

Lastly, sea-level rise vulnerability is negatively associated with cross-scale path lengths and positively associated with the logarithm of cross-scale network density (Table 3). The cross-scale ties show a more nuanced example of scale-dependency because the negative association between cross-level path length and problem severity is strongest for local subregional ties. Instead, the negative correlation with sea-level rise vulnerability suggests that the bridges to local actors are more responsive to problem severity. This finding complements the finding of a stronger relationship between problem severity and bonding social capital at the local level. In other words, local actors form more close-knit network configurations when they are more vulnerable to sea-level rise; concurrently, subregional actors act as intermediaries between the core and the periphery precisely in those OLUs that are more vulnerable.

CONCLUSION

We focused on the idea of scale dependency in policy networks in polycentric governance systems. We contribute to the literature by providing some theoretical rationale for expecting scale dependency, which is related to the benefits and transaction costs of forming policy networks experienced by policy actors at different levels of geographic scale. These theoretical ideas are related to the more general concept of scale dependency examined in ecology and complex systems. We provide an empirical approach for studying scale-dependency by slicing networks into different levels of geographic scale depending on the scope of policy actors’ jurisdictions or interests. The methodology allows us to study multiple networks across different geographies that vary in social-ecological attributes, which is a more powerful research design than studying just a single network. Such an approach can be replicated in other systems to assess the generality of our findings.

The findings provide interesting evidence of scale-dependency. There is evidence that including regional actors in networks is an important source of both bridging and bonding social capital. Regional actors are crucial for conferring a core-periphery type of structure to polycentric systems, linking local actors to the system, and facilitating processes of cooperation, learning, and information diffusion. The more responsive relationship between problem severity and local network structure is a crucial ingredient for linking the local and regional actors. The evidence is consistent with the idea that sea-level rise vulnerability motivates local actors to build bonding social capital that facilitates cooperation along with cross-level ties that link to higher levels of geographic scale. Regional actors are also more likely to target resources toward more vulnerable local areas. All these patterns are consistent with the theoretical perspectives on polycentric governance and adaptive governance in which bridging and bonding social capital are crucial ingredients for more resilient systems.

We found that responsiveness to problem severity is scale dependent, but our conclusions depend on how we think about spatial autocorrelation. In the presence of local network externalities, it is hard to detect the role of contextual factors in stimulating network evolution as the spatial regression model suggested. However, we do not believe that the presence of strong local network externalities means that contextual factors like SLR vulnerability are unimportant. Although network externalities implied by spatial autocorrelation suggest social feedbacks, it seems unlikely that the networks experienced some type of "spontaneous combustion." In other words, there must be some type of “spark” that stimulates the creation of some local networks, which then may generate spatial spillovers. Especially based on existing qualitative research (Lubell et al. 2021), we believe that problems associated with SLR risk are a catalyst for network formation.

The findings are also consistent with our substantive, qualitative understanding of institutional change for sea-level rise adaptation in the SF Bay system. As documented in Lubell and Robbins (2021), the polycentric system is rapidly growing and experiencing a process of decentralization with the emergence of many local actors and policy venues, and regional actors connecting to those local venues rather than local actors connecting to regional venues. The policy implications are that regional actors should take actions that reduce the transaction costs of building these types of policy networks, for example, by providing public goods, such as funding to facilitate local adaptation planning and projects, and disseminating scientific knowledge across the region. It also supports the overall policy discourse that more resources should be invested in those disadvantaged communities facing higher transaction costs for economic and cultural reasons.

Of course, the limitations of this analysis must be considered. We face the typical problem of survey non-response, which means we have not fully observed these networks. Although it is challenging to increase survey response rates in policy studies of this type, researchers in other regions or countries may discover different patterns. Measurement approaches that rely on archival data from project records or planning documents may also provide clearer evidence. We also cannot make any strong causal statements, such as sea-level rise vulnerability or other types of problem severity being a catalyst or stimulus for network development. It is important to note that this study only investigates how policy network structures are scale dependent. Although these structures are associated with processes like cooperation and learning, future work should more explicitly measure function. Additionally, although we estimate models that control for spatial autocorrelation, we cannot estimate models that directly test for different mechanisms that may create such spatial effects. Future research design, measurement, and model specification should consider how to best distinguish between different explanations such as network externalities, common exposure, and others. Lastly, more research is needed in other systems. We expect that some type of scale dependency is probably common in policy networks in polycentric systems, but there may be different types or classes of patterns. Overall, the theoretical importance of the idea of scale dependence plus the initial evidence reported here justifies further investigation.

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