Incorporating variability in simulations of seasonally forced phenology using integral projection models.

Phenology models are becoming increasingly important tools to accurately predict how climate change will impact the life histories of organisms. We propose a class of integral projection phenology models derived from stochastic individual-based models of insect development and demography. Our derivation, which is based on the rate summation concept, produces integral projection models that capture the effect of phenotypic rate variability on insect phenology, but which are typically more computationally frugal than equivalent individual-based phenology models. We demonstrate our approach using a temperature-dependent model of the demography of the mountain pine beetle ( Hopkins), an insect that kills mature pine trees. This work illustrates how a wide range of stochastic phenology models can be reformulated as integral projection models. Due to their computational efficiency, these integral projection models are suitable for deployment in large-scale simulations, such as studies of altered pest distributions under climate change.