Modelling the spatiotemporal dynamics of multispecies population interactions in the context of climate change

1. Species interactions are fundamental to the stability and productivity of ecosystems. To improve our capacity to predict and understand how climate change shapes the distribution of species and the dynamics of biotic interactions, we need to develop spatially explicit multi-species models that are built upon species-specific responses to changing conditions. 2. We developed a two-dimensional diffusion-advection-reaction predator-prey model that integrates species-specific responses to heterogeneous landscapes, affecting species dispersal, reproduction and survival rates. We derived conditions for the stability and feasibility of the coexistence steady-state and observed how temperature variation stabilises or destabilises the system. 3. We conducted numerical simulations to explore the effect of predicted extreme temperatures on the spatial dynamics of a parasitoid-butterfly system and their interactions. Applied to four different climatic environments, the numerical approximations demonstrate the asymmetric impact of a warming climate on interacting species. The output density distribution maps highlight the capability of our model to produce interpretable multiscale predictions which can be used to identify and evaluate species vulnerability locally and across their range. 4. By building upon a solid mechanistic understanding of species-specific responses to environmental change, our model can be extended to other species and variables, including environments where the availability of empirical data is limited, and explore the dynamics and distribution of interacting species under different scenarios of environmental change. ### Competing Interest Statement The authors have declared no competing interest.