Modeling the Evolution of Insect Phenology with Particular Reference to Mountain Pine Beetle

Climate change is likely to disrupt the timing of developmental events (phenology) in insect populations in which development time is largely determined by temperature. Shifting phenology puts insects at risk of being exposed to seasonal weather extremes during sensitive life stages and losing synchrony with biotic resources. Additionally, warming may result in loss of developmental synchronization within a population, making it difficult to find mates or mount mass attacks against well-defended resources at low population densities. It is unknown whether genetic evolution of development time can occur rapidly enough to moderate these effects. The work presented here is largely motivated by the need to understand how mountain pine beetle (MPB) populations will respond to climate change. MPB is an important forest pest from both an economic and ecological perspective, because MPB outbreaks often result in massive timber loss. Recent MPB range expansion and increased outbreak frequency have been linked to warming temperatures. We present a novel approach to modeling the evolution of phenology by allowing the parameters of a phenology model to evolve in response to selection on emergence time and density. We also develop a temperature-dependent phenology model for MPB that accounts for multiple types of developmental variation: variation that persists throughout a life stage, random variation, and variation due to the MPB oviposition mechanism. This model is parameterized using MPB development time data from constant temperature laboratory experiments. We use Laplace\u27s method to approximate steady distributions of the evolution model under stable temperatures. Here the mean phenotype allows for parents and offspring to be oviposited at exactly the same time of year in consecutive generations. These results are verified numerically for both MPB and a two-stage model insect. The evolution model is also applied to investigate the evolution of phenology for MPB and the two-stage model insect under warming temperatures. The model predicts that local populations can only adapt to climate change if development time can adapt so that individuals can complete exactly one generation per year and if the rate of temperature change is moderate