Critical phenomena in the climate system can cause drastic changes in the state of planetary ecosystems as well the entire biosphere. There also are mechanisms through which the biosphere can make an effect on climate. In this manuscript, we study the nonlinear dynamics of the interaction of the climate system with the biosphere by linking an energy balance climate model to different species competition models. We develop an asymptotic approach to these models and investigate how migration strengthens biome stability and biodiversity. Moreover, we derive relations describing biome boundary shifts under global warming (or cooling) and check those relations against paleo data on plant biome location. Finally, the models demonstrate that critical rates of changes in the environmental temperature dynamics may shift biome stability.