CONTEXT: Poverty can result from complex social-ecological interactions where persistent feedback loops create resistant, unsustainable states. In dryland regions, agricultural innovations intended to break poverty traps can often neglect long-term environmental consequences, leading to a reinforcing cycle of degradation and poverty.

OBJECTIVE: This study investigates how cross-level dynamics in agricultural innovation systems generate and sustain poverty traps. We ask: (i) How do poverty traps emerge in agricultural innovation systems? (ii) What characterizes agents experiencing these traps? (iii) How can traps be avoided or overcome?

METHODS: We combine dynamical systems modeling (DSM) and agent-based modeling (ABM) to analyze poverty trap emergence. DSM uses bifurcation analysis to reveal system-level dynamics under two innovation scenarios: low-impact (“gentle”) and high-impact (“strong”). ABM simulates these scenarios, tracking agent attributes across runs and mapping them onto DSM parameter space to identify producers and innovators in poor or non-poor states. Comparing agent outcomes with DSM parameter space identifies characteristics of poor and non-poor states. Together, DSM captures system dynamics while ABM reflects heterogeneity, enabling targeted interventions to escape poverty traps.

RESULTS AND CONCLUSIONS: Under gentle innovations, poverty and well-being depend on thresholds in innovation efficiency, funding, and desire: below thresholds, poverty is inevitable, at intermediate levels, outcomes depend on farmers' initial conditions and above thresholds, all reach well-being. Strong innovations carry higher ecological risks, with traps arising whenever thresholds are unmet. Low efficiency traps all farmers with fragile bistability and oscillating well-being at higher efficiencies. Low innovation funding and desire creates poor equilibria with stable well-being at higher levels. Improving innovation efficiency, through stronger knowledge efficiency (understanding producers' needs), greater innovation demand, and higher capital efficiency (better use of resources), increases the effectiveness of innovations and enables producers to escape poverty traps. Similarly, increasing innovation funding and demand for low-environmental-impact agricultural technologies supports pathways out of poverty by simultaneously improving income, ecological indicators, and crop production.

SIGNIFICANCE: This study highlights the critical role of agricultural innovation in shaping poverty trap dynamics and environmental outcomes. By focusing on cross-level interactions between micro-level producers and meso-level innovators, the study demonstrates how these interactions can create or sustain poverty traps. It emphasizes the importance of ecological feedback for understanding the long-term effects of interventions aimed at reducing poverty. Finally, it identifies pathways for breaking poverty traps that go beyond low-impact innovations, highlighting the need for systemic, coordinated interventions to achieve sustainable and resilient agricultural development.

This open access book is about causal thinking and the use of causal language, with a focus on introducing philosophical ideas about causation to students and researchers of Social-Ecological Systems (SES). It takes a systematic approach to three central topics: the meanings of different causal expressions, sufficiency of evidence for inferences from observations to causal relations, and how to handle the complexity of causal relations in social-ecological systems. Consequently, the book is divided into three parts. In the first part the authors analyse and discuss the use of causal idiom in ordinary language, and in the second part they scrutinise the use of causal concepts and causal inference in science. Finally, the authors discuss causal reasoning about social-ecological systems in multi- and interdisciplinary contexts.

Understanding causation in social-ecological systems (SES) is indispensable for promoting sustainable outcomes. However, the study of such causal relations is challenging because they are often complex and intertwined, and their analysis involves diverse disciplines. Although there is agreement that no single research approach (RA) can comprehensively explain SES phenomena, there is a lack of ability to deal with this diversity. Underlying this diversity and the challenge of dealing with it are different causal reasonings that are rarely explicit. Awareness of hidden assumptions is essential for understanding how the causal reasoning of an RA is constituted, and for promoting the integration, translation, or juxtaposition of different RAs. We identify the following elements as particularly relevant for understanding causal reasoning: methods, frameworks and theories, accounts of causation, analytical focus, and causal notions. We begin with the idea that one of these elements typically figures as an entry point to an RA. This entry point is particularly important because it generates a path dependence that orients causal reasoning. In a subsequent step, when an approach is applied, causal reasoning concretizes as a result of a particular constellation of the remaining elements. We come to these insights by studying the application of four different RAs to the same social-ecological case (the collapse of Baltic cod stocks in the 1980s). On the basis of our findings we developed a guide for the analysis of causal reasoning by raising awareness of the assumptions, key elements, and the relations between these key elements for a given RA. The guide can be used to elicit the causal reasoning of RAs, facilitate interdisciplinary collaboration, and support disclosure of ethical/political dimensions that underlie management/governance interventions that are formulated on the basis of causal findings of research studies.

When reasoning about causes of sustainability problems and possible solutions, sustainability scientists rely on disciplinary-based understanding of cause–effect relations. These disciplinary assumptions enable and constrain how causal knowledge is generated, yet they are rarely made explicit. In a multidisciplinary field like sustainability science, lack of understanding differences in causal reasoning impedes our ability to address complex sustainability problems. To support navigating the diversity of causal reasoning, we articulate when and how during a research process researchers engage in causal reasoning and discuss four common ideas about causation that direct it. This articulation provides guidance for researchers to make their own assumptions and choices transparent and to interpret other researchers’ approaches. Understanding how causal claims are made and justified enables sustainability researchers to evaluate the diversity of causal claims, to build collaborations across disciplines, and to assess whether proposed solutions are suitable for a given problem.

Social-ecological systems research aims to understand the nature of social-ecological phenomena, to find ways to foster or manage conditions under which desired phenomena occur or to reduce the negative consequences of undesirable phenomena. Such challenges are often addressed using dynamical systems models (DSM) or agent-based models (ABM). Here we develop an iterative procedure for combining DSM and ABM to leverage their strengths and gain insights that surpass insights obtained by each approach separately. The procedure uses results of an ABM as inputs for a DSM development. In the following steps, results of the DSM analyses guide future analysis of the ABM and vice versa. This dialogue, more than having a tight connection between the models, enables pushing the research frontier, expanding the set of research questions and insights. We illustrate our method with the example of poverty traps and innovation in agricultural systems, but our conclusions are general and can be applied to other DSM-ABM combinations.

Dynamical systems modeling (DSM) explores how a system evolves in time when its elements and the relationships between them are known. The basic idea is that the structure of a dynamical system, expressed by coupled differential or difference equations, determines attractors of the system and, in turn, its behavior. This leads to structural understanding that can provide insights into qualitative properties of real systems, including ecological and social-ecological systems (SES). DSM generally does not aim to make specific quantitative predictions or explain singular events, but to investigate consequences of different assumptions about a system's structure. SES dynamics and possible causal relationships in SES get revealed through manipulation of individual interactions and observation of their consequences. Structural understanding is therefore particularly valuable for assessing and anticipating the consequences of interventions or shocks and managing transformation toward sustainability. Taking into account social and ecological dynamics, recognizing that SES may operate on different time scales simultaneously and that achieving an attractor might not be possible or relevant, opens up possibilities for DSM setup and analysis. This also highlights the importance of assumptions and research questions for model results and calls for closer connection between modeling and empirics. Understanding the potential and limitations of DSM in SES research is important because the well-developed and established framework of DSM provides a common language and helps break down barriers to shared understanding and dialog within multidisciplinary teams. In this primer we introduce the basic concepts, methods, and possible insights from DSM. Our target audience are both beginners in DSM and modelers who use other model types, both in ecology and SES research.

Models are widely used for investigating cause-effect relationships in complex systems. However, often different models yield diverging causal claims about specific phenomena. Therefore, critical reflection is needed on causal insights derived from modeling. As an example, we here compare ecological models dealing with the dynamics and collapse of cod in the Baltic Sea. The models addressed different specific questions, but also vary widely in system conceptualization and complexity. With each model, certain ecological factors and mechanisms were analyzed in detail, while others were included but remained unchanged, or were excluded. Model-based causal analyses of the same system are thus inherently constrained by diverse implicit assumptions about possible determinants of causation. In developing recommendations for human action, awareness is needed of this strong context dependence of causal claims, which is often not entirely clear. Model comparisons can be supplemented by integrating findings from multiple models and confronting models with multiple observed patterns.

In social-ecological systems (SES), where social and ecological processes are intertwined, phenomena are usually complex and involve multiple interdependent causes. Figuring out causal relationships is thus challenging but needed to better understand and then affect or manage such systems. One important and widely used tool to identify and communicate causal relationships is visualization. Here, we present several common visualization types: diagrams of objects and arrows, X-Y plots, and X-Y-Z plots, and discuss them in view of the particular challenges of visualizing causation in complex systems such as SES. We use a simple demonstration model to create and compare exemplary visualizations and add more elaborate examples from the literature. This highlights implicit strengths and limitations of widely used visualization types and facilitates adequate choices when visualizing causation in SES. Thereupon, we recommend further suitable ways to account for complex causation, such as figures with multiple panels, or merging different visualization types in one figure. This provides caveats against oversimplifications. Yet, any single figure can rarely capture all relevant causal relationships in an SES. We therefore need to focus on specific questions, phenomena, or subsystems, and often also on specific causes and effects that shall be visualized. Our recommendations allow for selecting and combining visualizations such that they complement each other, support comprehensive understanding, and do justice to the existing complexity in SES. This lets visualizations realize their potential and play an important role in identifying and communicating causation.

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number R0R0 for time-independent and periodical models and establish the permanence dichotomy: if R0≤1R0≤1, extinction on all patches is imminent, and if R0>1R0>1, permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.

Recent research has demonstrated the multidimensional nature of poverty and the multi-level organization of social-ecological systems that display poverty traps. The traps on these different levels can reinforce each other, and therefore multi-level traps pose particular challenges for poverty alleviation. Yet, poverty trap models rarely consider more than one level of organization and only a few attributes of the system at each level. These limitations constrain our understanding of the mechanisms that generate poverty traps and may hinder or even mislead development efforts. Here, we present a series of two-level dynamical system models of poverty traps and use these models to investigate the combined influences of biophysical and economic factors, farmers’ habits and community decisions on creating and alleviating persistent poverty. Our results indicate that neglecting key interactions can lead to incorrect assessments and potentially inadequate alleviation strategies. Moreover, we obtain necessary conditions for the existence of fractal poverty traps, and show that (i) cross-level interactions can open possibilities for escaping from poverty, (ii) that farmers’ behavioral changes may create or impede a way out of poverty, and (iii) that the effectiveness of development interventions depends on the combined influences of biophysical and economic dynamics, farmers’ behavior and community spending on agricultural and social activities.