Social-ecological network analysis for sustainability sciences: a systematic review and innovative research agenda for the future

Social-ecological network (SEN) concepts and tools are increasingly used in human-environment and sustainability sciences. We take stock of this budding research area to further show the strength of SEN analysis for complex human-environment settings, identify future synergies between SEN and wider human-environment research, and provide guidance about when to use different kinds of SEN approaches and models. We characterize SEN research along a spectrum specifying the degree of explicit network representation of system components and dynamics. We then systematically review one end of this spectrum, what we term “fully articulated SEN” studies, which specifically model unique social and ecological units and relationships. Results show more focus on methodological advancement and applied ends. While there has been some development and testing of theories, this remains an area for future work and would help develop SENs as a unique field of research, not just a method. Authors have studied diverse systems, while mainly focused on the problem of social-ecological fit alongside a scattering of other topics. There is strong potential, however, to engage other issues central to human-environment studies. Analyzing the simultaneous effects of multiple social, environmental, and coupled processes, change over time, and linking network structures to outcomes are also areas for future advancement. This review provides a comprehensive assessment of (fully articulated) SEN research, a necessary step that can help scholars develop comparable cases and fill research gaps.

network extent, in which researchers, once having identified a logical social and/or ecological starting point followed the network until its logical end (from a social network methodological perspective, this would most likely be done using "snowball" sampling, for example); or "other." Through the last category, two additional bounding approaches emerged: some modeling studies were based on a theoretical universe and thus, had an abstract or theoretical bounding. Several studies also were bound by what we call the social-ecological system. In this last case, not all social or all ecological units in a given arena are included in the network, but rather specific actors, organizations, or institutions were selected alongside corresponding resource units, habitat patches, or other environmental areas based on an a priori detailed understanding of the socialecological system. Finally, the kind of evidence used in the paper included empirical investigation though field work or "desk methods" (e.g., document coding), simulation and modeling work, synthesis of existing published case studies, or "other" of which no alternatives were identified. Methods were open coded and inductively fit into categories. All variables allowed for multiple coded responses, except for study system and system bounding.
Our second line of inquiry, how fully articulated SENs are constructed, focused on the kinds of nodes and edges in the network and how the networks were conceptualized according to section 2.2. We categorized social nodes to illustrate different kinds of social actors or phenomena including individuals, households, and organizations, as the choice to focus on individual versus collective entities (e.g., organizations) impacts what can be learned about the underlying social dynamics (Butts 2009, Newig et al 2010, Sayles and Baggio 2017b. We also considered policies/laws and human management actions as other social entities that are often represented in SENs (e.g., Ekstrom and Young 2009) and allowed for additional write-in responses. Ecological nodes were classified as individual plant/animals, groups of plant/animals, specific habitat patches, biophysical places/areas, concepts of habitats/ecosystems, plus the option of an "other" write-in response. These categories capture a wide range of ways that researchers might represent the environment and were also informed by experiences that some physical phenomena more readily translated into the concepts of nodes. For example, small discrete forest patches or wetlands naturally form a network, whereas other biophysical phenomena, like surface hydrology or forest fires, are a more contiguous biophysical surface and require different assumptions to translate into nodes and edges (Sayles and Baggio 2017a, Turnbull et al 2018, Hamilton et al 2019. These might be seen as biophysical places or areas.
We categorized social edges based on the general type of relationship they represented. Following Borgatti et al (2009), we distinguished between nominal relationships, those representing social roles such as friends, partners, or collaborators, and those representing flows such as information, financial, or resources sharing. We included measures of performance as a unique category given the importance of outcome metrics for advancing environmental network research (Barnes et al 2016, Groce et al 2019, as well as a category on concepts of trust and legitimacy as these are important drivers of institutional structure (Berardo andScholz 2010, Lubell et al 2014). Other write-in responses were permitted. Ecological edges were classified as movement of plants and animals, movement of water, sediment, or biophysical materials, trophic interactions, concepts of ecosystem / environmental linkages, and allowed for an "other" write-in response. These codes illustrate the different ways authors might depict ecological interactions as both real and conceptual systems and in discrete or contiguous landscapes (Sayles and Baggio 2017a, Turnbull et al 2018, Hamilton et al 2019. Finally, we defined social-ecological edges in a similar manner to how social edges were defined, by focusing on the character of relationships and interactions embodied by the edge. We considered relationships of ownership or management, which are similar to the social category of nominal, where the relationship between the social and ecological node was defined based on the social node having management jurisdiction or working in a given ecological area. We then considered different types of agency and flow. Harvest relationships described relationships that would not exist without action by social nodes (e.g., harvest or extraction). Supporting/regulating relationships described the flow of ecological processes back to the social node independent of the social node's activity (e.g., storm protection or carbon sequestration), though we acknowledge and recognize that the social node must be in a spatial or power relationship, or both, that allows for benefits. Reciprocal relationships described co-produced interactions that cannot be reduced to the social node acting on the ecological, or the ecological flowing to the social without social agency. While arguably all social-ecological relationships are co-produced, the distinction here is on the dominant direction of agency or flow in creating the relationship. For example, there is a categorical distinction between something like resource extraction (harvest category) and spiritual value, sense of place, and recreational fulfillment (reciprocal category). Of course, the two are not mutually exclusive; someone can find spiritual value through their resource extraction (and the edge would be coded as representing two phenomena). Other write-in responses were also permitted. All node and edge variables allowed for multiple coded responses.

SI.3 Inventory of nodes and edges used to construct SENs
The pairing of social and ecological nodes and edges illustrates how authors have constructed SEN. The following figures present the count of specific node and edge pairings.

SI.4 Details of the citation network analysis
To understand the cohesiveness of fully articulated SEN research we conducted a citation network analysis. We did not expect all papers to be linked through direct citations, but did expect papers to draw from common theoretical works. We therefore constructed a bibliometric network of fully articulated SEN papers and their cited references to look at their common intellectual roots. We reduced the network to consider only cited papers with at least two citations, omitting citations that did not bind the network together. We used Freeman's degree centrality, which considers the number of cited references (fully articulated SEN papers only) and citations (for all papers). Only considering citation count (i.e., indegree centrality) would omit new SEN papers (e.g., Bergsten et al 2019, Hamilton et al 2019) that had not yet accrued citations. We then analyzed citation patterns using indegree centrality to understand which papers were common among SEN articles. Analysis was done in the R language environment using the packages network and sna (Butts 2015(Butts , 2016. The following figures show the full citation network prior to reduction by Freeman's degree centrality, the reduced network with all nodes labeled by IDs, and corresponding table of 22 fully articulated SEN papers and common cited references.  . We removed all references that were only cited by a single SEN paper and thus, not uniting the network. Nodes are labeled using network ID values, which correspond to citations in table S1.