Seasonal temperature alone can synchronize life cycles

In this paper we discuss the effects of yearly temperature variation on the development and seasonal occurrence of poikiliothermic organisms with multiple life stages. The study of voltinism in the mountain pine beetle (Dendroctonus ponderosae Hopkins), an important forest insect living in extreme temperature environments and exhibiting no diapause, provides a motivational example. Using a minimal model for the rates of aging it is shown that seasonal temperature variation and minimal stage-specific differences in rates of aging are sufficient to create stable uni- and multi-voltine oviposition cycles. In fact, these cycles are attracting and therefore provide an exogenous mechanism for synchronizing whole populations of organisms. Structural stability arguments are used to extend the results to more general life systems. (C) 2000 Society for Mathematical Biology.