Many resource management studies focus on one resource. Humans, however, rely on multiple resources in a complicated way. A person may derive more well-being from one unit of a resource than from another; one resource may be substituted by another to some degree. How should one manage such coupled natural-human systems? In this work, we build on recent research that focuses on developing conceptual frameworks and mathematical models to understand such interactions. The multiple resource condition injects the concept of substitutability into models of coupled human-natural systems and affects how such systems should be governed. Substitutability has been mostly mentioned in the field of economics for a substitution of natural and human capitals. Similarly, one resource may substitute for other scarce resources in coupled human-natural systems since some of these resources are not completely independent. In this study, we revise and expand an existing conceptual framework to include two natural resources, resource users, governing agency and public infrastructure in a centralized governance structure, i.e., all the natural resources are managed by the same governing entity. We then devise a set of dynamical equations and relationships from different fields, such as a replicator equation, a population equation, and a CES production equation, to capture the dynamics of this coupled system. This analysis can provide a decision-support tool to design policies to sustainably govern the built environment where human, natural resources, and infrastructure are interconnected. Model analysis takes a multi-faceted perspective of both resource users and governing entities to assess policies against different levels of disturbance. The results reveal how substitutability and asymmetry in resource use affect the viable policies needed to maintain the system.

Migration is a complex and interdisciplinary problem involving multiple factors such as social interactions, resource scarcity, and geographical features. These factors must be incorporated in migration models, but how? We feel that the issue how different factors should be incorporated is not carefully addressed in existing models. Configuring factors in ways that are theoretically unsound can lead to false migration patterns and undermine the usefulness of models; indeed, factor configurations may be more critical than the factors themselves or other inputs. Therefore, we ask: i) How important is factor configuration to output results comparing with other inputs?; ii) How do different factor configurations produce different migration patterns?; and iii) How can multimodality of certain output distributions be controlled in a management perspective? To address the questions, we develop a “toy” migration agent-based model (ABM) and explore three possible configurations between two factors: i) two factors are perfectly substitutable (ADD), ii) both factors are indispensable (AND), and iii) either is enough (OR). ABM results are analyzed by global sensitivity analysis (GSA) and Monte-Carlo Filtering (MCF). The relative importance of factor configurations quantified by GSA emphasizes why we need to consider how the factors are incorporated. Depending on factor configurations, we also observe unimodal or multimodal output distributions. MCF is then applied to the ABM-GSA results to address how policymakers should control certain inputs to sustain systems with desirable outputs. Altogether, we have integrated ABM, GSA, and MCF to disentangle complexity of migration models and better understand underlying mechanisms and patterns of migration.