Archaeological settlement patterns are the physical remains of complex webs of human decision-making and social interaction. Entropy-maximizing spatial interaction models are a means of building parsimonious models that average over much of this small-scale complexity, while maintaining key large-scale structural features. Dynamic social interaction models extend this approach by allowing archaeologists to explore the co-evolution of human settlement systems and the networks of interaction that drive them. Yet, such models are often imprecise, relying on generalized notions of settlement ‘influence’ and ‘attractiveness’ rather than concrete material flows of goods and people. Here, I present a dis-aggregated spatial interaction model that explicitly resolves trade and migration flows and their combined influence on settlement growth and decline. I explore how the balance of costs and benefits of each type of interaction influence long-term settlement patterns. I find trade flows are the strongest determinant of equilibrium settlement structure, and that migration flows play a more transient role in balancing site hierarchies. This model illustrates how the broad toolkit for spatial interaction modeling developed in geography and economics can increase the precision of quantitative theory building in archaeology, and provides a road-map for connecting mechanistic models to the empirical archaeological record.