The study of social-ecological systems (SES) has been significantly shaped by insights from research on complex adaptive systems (CAS). We offer a brief overview of the conceptual integration of CAS research and its implications for the advancement of SES studies and methods. We propose a conceptual typology of six organizing principles of CAS based on a comparison of leading scholars' classifications of CAS features and properties. This typology clusters together similar underlying organizing principles of the features and attributes of CAS, and serves as a heuristic framework for identifying methods and approaches that account for the key features of SES. These principles can help identify appropriate methods and approaches for studying SES. We discuss three main implications of studying and engaging with SES as CAS. First, there needs to be a shift in focus when studying the dynamics and interactions in SES, to better capture the nature of the organizing principles that characterize SES behavior. Second, realizing that the nature of the intertwined social-ecological relations is complex has real consequences for how we choose methods and practical approaches for observing and studying SES interactions. Third, engagement with SES as CAS poses normative challenges for problemoriented researchers and practitioners taking on real-world challenges.

Abstract. Protected areas (PAs) remain central to the conservation of biodiversity. Classical PAs were conceived as areas that would be set aside to maintain a natural state with minimal human influence. However, global environmental change and growing cross-scale anthropogenic influences mean that PAs can no longer be thought of as ecological islands that function independently of the broader social-ecological system in which they are located. For PAs to be resilient (and to contribute to broader social-ecological resilience), they must be able to adapt to changing social and ecological conditions over time in a way that supports the long-term persistence of populations, communities, and ecosystems of conservation concern. We extend Ostrom's social-ecological systems framework to consider the long-term persistence of PAs, as a form of land use embedded in social-ecological systems, with important crossscale feedbacks. Most notably, we highlight the cross-scale influences and feedbacks on PAs that exist from the local to the global scale, contextualizing PAs within multi-scale socialecological functional landscapes. Such functional landscapes are integral to understand and manage individual PAs for long-term sustainability. We illustrate our conceptual contribution with three case studies that highlight cross-scale feedbacks and social-ecological interactions in the functioning of PAs and in relation to regional resilience. Our analysis suggests that while ecological, economic, and social processes are often directly relevant to PAs at finer scales, at broader scales, the dominant processes that shape and alter PA resilience are primarily social and economic.

Key methods discussed in this chapterModelling methods: System dynamics (group model building, mediated modelling, shared vision planning), agent-based models (ARDI), role-playing games (Wat-A-Game), expert models (Bayesian networks, fuzzy cognitive maps), state-and-transition models, soft system methodologies (rich pictures, concept maps, decision trees, cognitive maps) Integrated approaches: Collaborative modelling, companion modelling, participatory system analysis Connections to other chaptersMethods for generating data and systems scoping (Chapters 5-8), specifically participatory data-collection methods (Chapter 8) or interviews and surveys (Chapter 7), may provide working material or monitoring and evaluation support within participatory modelling processes. Facilitated dialogue methods (Chapter 9) may smooth participatory modelling workshops. Future analysis (Chapter 10), scenario development (Chapter 11) or serious games (Chapter 12) may be articulated with participatory models within broader participatory resilience assessment (Chapter 14) or action research (Chapter 15) projects. Expert modelling (Chapter 16), dynamical systems modelling (Chapter 26), state-and-transition modelling (Chapter 27) and agent-based modelling (Chapter 28) cover the most common types of modelling methods used in participatory modelling, and participatory modelling may use institutional analysis (Chapter 22) conceptual frameworks.

The effectiveness of parks for forest conservation is widely debated in Africa, where increasing human pressure, insufficient funding, and lack of management capacity frequently place significant demands on forests. Tropical forests house a substantial portion of the world's remaining biodiversity and are heavily affected by anthropogenic activity. We analyzed park effectiveness at the individual (224 parks) and national (23 countries) level across Africa by comparing the extent of forest loss (as a proxy for deforestation) inside parks to matched unprotected control sites. Although significant geographical variation existed among parks, the majority of African parks had significantly less forest loss within their boundaries (e.g., Mahale Park had 34 times less forest loss within its boundary) than control sites. Accessibility was a significant driver of forest loss. Relatively inaccessible areas had a higher probability (odds ratio >1, p < 0.001) of forest loss but only in ineffective parks, and relatively accessible areas had a higher probability of forest loss but only in effective parks. Smaller parks less effectively prevented forest loss inside park boundaries than larger parks (T = -2.32, p < 0.05), and older parks less effectively prevented forest loss inside park boundaries than younger parks (F = -4.11, p < 0.001). Our analyses, the first individual and national assessment of park effectiveness across Africa, demonstrated the complexity of factors (such as geographical variation, accessibility, and park size and age) influencing the ability of a park to curb forest loss within its boundaries.

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