Sustainability or Otherwise: The Lotka-Volterra Model in Population Ecology and Socio-Economic Systems

Abstract The Lotka-Volterra equations, a cornerstone of predator-prey modeling, offer a versatile framework for understanding population dynamics in the context of sustainability. This chapter explores how these equations, through the analysis of dynamic equilibrium and stability, illuminate principles of both sustainable ecological interactions and the mechanisms leading to detrimental long-term out-comes in various systems (negative sustainability). We first analyze predator-prey interactions to gain insights into population management, resource conservation, and the delicate balance of ecosystems. Furthermore, we extend the Lotka-Volterra model to discuss its broader implications for complex systems dynamics in diverse fields, such as in modeling economic competition and arms races, where the framework helps identify pathways that lead to unsustainable resource consumption, increased risk, or collapse. Competing Interest Statement The authors have declared no competing interest. Footnotes A subsection on oscillation period added; the section on pedagogy removed; applications extended to include both positive and negative sustainability scenarios.