The Iceberg study suggests that new spillovers will follow surprising rules. For example, the team assumed that these events would be concentrated in the Arctic because warming temperatures nudge animals toward higher, cooler latitudes. But if two species move northward in parallel, nothing changes. The real drama occurs, for instance, when animals seek higher, cooler altitudes, and when those living on opposite sides of a mountain meet in the middle. This means that spillovers will be concentrated not in the poles, but in the mountainous and species-rich parts of tropical Africa and southeast Asia.

Southeast Asia will also be especially spillover-prone because it’s home to a wide range of bats. Flight gives bats flexibility, allowing them to react to changing climates more quickly than other mammals, and to carry their viruses farther. And bats in Southeast Asia are highly diverse, and tend to have small ranges that don’t overlap. “You shake that like a snowglobe and you get a lot of first encounters,” Carlson said.

Such events will also be problematic elsewhere in the world. In Africa, bats are probably the natural reservoirs for Ebola. Thirteen species could potentially carry the virus, and as global warming forces them to disperse, they’ll encounter almost 3,700 new mammal species, leading to almost 100 spillovers. So far, the biggest Ebola outbreaks have occurred in West Africa, but Carlson said that within decades, the disease could easily become a bigger problem for the continent’s eastern side too. “And that’s emblematic of everything,” he told me: Every animal-borne disease will likely change in similarly dramatic ways.