The large-scale geometry and age progression of many hotspot island chains, such as the Hawaiian–Emperor chain, are well explained by the steady movement of tectonic plates over stationary hotspots. But on a smaller scale, hotspot tracks are composed of discrete volcanic islands whose spacing correlates with lithospheric thickness1. Moreover, the volcanic shields themselves are often not positioned along single lines, but in more complicated patterns, such as the dual line known as the Kea and Loa trends of the Hawaiian islands2, 3. Here we make use of the hypothesis that island spacing is controlled by lithospheric flexure1 to develop a simple nonlinear model coupling magma flow, which feeds volcanic growth, to the flexure caused by volcanic loads on the underlying plate. For a steady source of melt underneath a moving lithospheric plate, magma is found to reach the surface and build a chain of separate volcanic edifices with realistic spacing. If a volcano is introduced away from the axis of the chain, as might occur following a change in the direction of plate motion, the model perpetuates the asymmetry for long distances and times, thereby producing an alternating series of edifices similar to that observed in the Kea and Loa trends of the Hawaiian island chain.