Species distribution models (SDMs) are used to predict species distributions and abundances. Despite their extensive use and considerable advancements over the past few decades, they are still limited in their abilities to incorporate important biological realities, such as biotic interactions and evolutionary change. In this thesis, I develop several mechanistic models which explicitly account for biotic interactions and/or evolutionary adaptation for an aphid-ladybird predator-prey system. Across these chapters, I examine the complex interactions between biological interactions, evolution and climate change.

First, I develop a temperature-dependent stage-structured population dynamic model for aphids and ladybirds in Chapter 2. I use this model to examine predation's effect on the abundance of aphids with climate change. I find that the effect of predation on aphid abundance will generally decrease relative to the effect of climate when future climates become warmer and more seasonal. In Chapter 3, I use Chapter 2's model as a basis for mechanistic SDMs to compare with an ensemble of correlative SDMs to predict the distributions and abundances of five aphid species. The comparison between the two modeling approaches is informative about the necessity of accounting for biotic interactions and the interplay between abiotic and biotic factors when predicting distributions. Lastly, I develop an eco-evolutionary model to examine the effect of evolutionary adaptation in an aphid-ladybird predator-prey system under climate change (Chapter 4) and apply it to a representative set of geographic locations in the United States. The results show that there is geographic variation in evolutionary rescue for ladybirds across locations, which points to the importance of incorporating evolutionary adaptation in SDMs. The three chapters contribute to the contemporary development of SDMs by offering valuable theoretical extensions, particularly those considering biotic interactions and species' adaptation to climate change.