A general framework for stock dynamics of populations and built and natural environments

Abstract

Sustainable development involves a responsible management of the interactions between humans and their built and natural environment. From a physical perspective, the interactions can be characterized as stocks and flows of energy and matter within and between these spheres. Understanding the dynamics of the stocks is essential to enable their responsible management. A large number of independent disciplines study the dynamics of individual stocks with specific methods. The resulting fragmentation of methods hampers interdisciplinary learning, including the integration of more specialized discipline‐specific models into more encompassing ones. Here, we develop a general mathematical framework for dynamic stock models based on balance, intrinsic, and model‐approach equations. We use the framework to classify a variety of stock models from different disciplines and discuss their applicability. The framework provides a common language for the interdisciplinary analysis of coupled human–environment systems. This article met the requirements for a gold‐gold JIE data openness badge described at http://jie.click/badges.

A product–component framework for modeling stock dynamics and its application for electric vehicles and lithium‐ion batteries

“…Following the assumption that the products are providing the required service, and that it is the provision of the service that is driving the demand for the product (Müller, 2006), we use a stock‐driven model that allows us to investigate the system dynamics under different modeling assumptions (Lauinger et al., 2021). Figure 1 shows a generic system definition of products and components that allows investigating the dynamics of product reuse and repair by replacing failed components.…”

“…Case 7 : The lifetime approach is fully substituted by calculating the inflows and outflows with birth or death rates, the latter often being referred to as leaching approach (Lauinger et al., 2021). We introduce two cases denominated 7a where a death rate is used as a driver and 7b where a birth rate is used.…”

“…However, while these approaches allow to independently track the dynamics of multiple products and components, the combined dynamics and the role of the component in limiting or extending the product's useful time are not considered. Furthermore, the lifetime is usually modeled using the survival function, linking outflows and inflows by tracking the remaining fraction of a given cohort over time (Lauinger et al., 2021). Nevertheless, the life expectancy at birth of an individual does not directly determine the probability of dying in a given year.…”

Sector‐specific scenarios for future stocks and flows of aluminum: An analysis based on shared socioeconomic pathways

“…Stock projections were calculated from the inflow and the survival function. See Lauinger et al (2021) for a general framework regarding stock dynamics.…”

“…The reduced demand for cast aluminum arising from the electrification of transport (Hatayama et al., 2012; Modaresi et al., 2014; Rombach et al., 2012) may also consequently lead to a surplus of low‐grade recycled aluminum (Bertram et al., 2017; Hatayama et al., 2009; Rombach et al., 2012). These potential issues highlight the importance of understanding not only the aluminum stocks dynamics, but also those of its different alloys and alloying elements to improve the management of aluminum resources and to support the transformation of the industry toward a more sustainable and circular economy (Lauinger et al., 2021).…”