Modeling the evolution of insect phenology.

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. 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 use the Laplace method to find asymptotic approximations for the temporal variation in mean phenotype and phenotypic variance arising in the evolution model that are used to characterize invariant distributions of the model under periodic temperatures at leading order. At these steady distributions the mean phenotype allows for parents and offspring to be oviposited at the same time of year in consecutive years. Numerical simulations show that populations evolve to these steady distributions under periodic temperatures. We consider an example of how the evolution model predicts populations will evolve in response to warming temperatures and shifting resource phenology.