A Constraint-based model of Dynamic Island Biogeography: environmental history and species traits predict hysteresis in populations and communities We present a conceptual model that shows how hysteresis can emerge in dynamic island systems given simple constraints on trait-mediated processes. Over time, many islands cycle between phases of increasing and decreasing size and connectivity to a mainland species pool. As these phases alternate, the dominant process driving species composition switches between colonization and extinction. Both processes are mediated by interactions between organismal traits and environmental constraints: colonization probability is affected by a species’ ability to cross the intervening matrix between a population source and the island; population persistence (or extinction) is driven by the minimum spatial requirements for sustaining an isolated population. Because different suites of traits often mediate these two processes, similar environmental conditions can lead to differences in species compositions at two points of time. Thus, the Constraint-based model of Dynamic Island Biogeography (C-DIB) illustrates the possible role of hysteresis—the dependency of outcomes not only on the current system state but also the system’s history of environmental change—in affecting populations and communities in insular systems. The model provides a framework upon which additional considerations of lag times, biotic interactions, evolution, and other processes can be incorporated. Importantly, it provides a testable framework to study the physical and biological constraints on populations and communities across diverse taxa, scales, and systems.