Modeling the Fall of the Inca Empire: A Lotka–Volterra Approach to the Spanish Conquest

The Spanish conquest of the Inca empire in the early 16th century stands as one of the most striking examples of asymmetric historical collapse. In this paper, a simplified mathematical formulation is developed being inspired by Lotka–Volterra dynamics to describe, in a stylized quantitative manner, the interactions between the Inca state and the invading Spanish forces. The model is not intended to explain the historical events in a causal or predictive sense, but rather to capture and represent key mechanisms commonly identified in historical analyses. These include the demographic and political weakening caused by smallpox epidemics prior to direct contact, the internal fragmentation produced by the civil war and the introduction of external shocks such as the capture of Atahualpa and the fall of Cusco. Although intentionally minimalistic, the framework provides a dynamical illustration of how combined internal and external pressures can destabilize a complex society. This descriptive perspective situates the Inca collapse within the broader conceptual language of complex systems, emphasizing how nonlinear interactions, feedback and structural asymmetry shape trajectories of resilience and failure.