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The dynamics and adaptive capacity of social-ecological systems are heavily contingent on system structure, which is established through geography, institutions, interactions, and movement. Contrasting views of system structure, as hierarchies and single-level networks respectively, have tended to emphasize the role of either top-down or lateral (peer-to-peer) connections. The concept of a heterarchy aims to capture both top-down and lateral connections on orthogonal axes and has been proposed as a way of unifying alternative approaches to measuring structure, but it has not been fully operationalized for quantifying and comparing system structures. We developed a simple approach to consistently quantifying heterarchical structure across different kinds of networks. We first calculated suitable metrics, including modularity and a hierarchy score, for a wide range of both simulated and real-world systems including food webs, biological, infrastructure, and social networks. Metrics were corrected for differences in size and magnitude. The results were then visualized as a heterarchy matrix. We compared the angle (degrees) and Euclidian distance of each simulated and real-world network from the center of the matrix between network groups. All networks showed distinct placement on the heterarchy matrix. Relative to one another, food webs were laterally polycentric, social networks were mainly pyramidal and coordinated polycentric, and biological networks were pyramidal and laterally polycentric. Our test of concept, although relatively basic, provides strong evidence that system structure cannot be fully understood as purely laterally connected or purely hierarchical. System resilience requires a tradeoff between modularity, aiding redundancy and collaboration; and hierarchy, aiding efficient action. Our approach has the potential to provide a robust, accessible methodology to quantify system structure that allows for universal contextualization, a key step within fields such as resilience and sustainability science. [ABSTRACT FROM AUTHOR]

Complex networks of relationships among and between people and nature (social‐ecological networks) play an important role in sustainability; yet, we have limited empirical understanding of their temporal dynamics.We empirically examine the evolution of a social‐ecological network in a common‐pool resource system faced with escalating social and environmental change over the past two decades.We first draw on quantitative and qualitative data collected between 2002 and 2018 in a Papua New Guinean reef fishing community to provide contextual evidence regarding the extent of social and environmental change being experienced. We then develop a temporal multilevel exponential random graph model using complete social‐ecological network data, collected in 2016 and 2018, to test key hypotheses regarding how fishing households have adapted their social ties in this context of change given their relationships with reef resources (i.e. social‐ecological ties). Specifically, we hypothesized that households will increasingly form tight‐knit, bonding social and social‐ecological network structures (H1 and H3, respectively) with similar others (H2), and that they will seek out resourceful actors with specialized knowledge that can promote learning and spur innovation (H4).Our results depict a community that is largely 'bunkering down' and looking inward in response to mounting risk to resource‐dependent livelihoods and a breakdown in the collaborative processes that traditionally sustained them. Community members are increasingly choosing to interact with others more like themselves (H2), with friends of friends (H1), and with those connected to interdependent ecological resources (H3)—in other words, they are showing a strong, increasing preference for forming bonding social‐ecological network structures and interacting with like‐minded, similar others. We did not find strong support for H4.Bonding network structures may decrease the risk associated with unmonitored behaviour and help to build trust, thereby increasing the probability of sustaining cooperation over time. Yet, increasing homophily and bonding ties can stifle innovation, reducing the ability to adapt to changing conditions. It can also lead to clustering, creating fault lines in the network, which can negatively impact the community's ability to mobilize and agree on/enforce social norms, which are key for managing common resources. Read the free Plain Language Summary for this article on the Journal blog. Read the free Plain Language Summary for this article on the Journal blog. [ABSTRACT FROM AUTHOR]