Support for an extremist entity such as Islamic State (ISIS) somehow manages to survive globally online despite considerable external pressure and may ultimately inspire acts by individuals having no history of extremism, membership in a terrorist faction, or direct links to leadership. Examining longitudinal records of online activity, we uncovered an ecology evolving on a daily time scale that drives online support, and we provide a mathematical theory that describes it. The ecology features self-organized aggregates (ad hoc groups formed via linkage to a Facebook page or analog) that proliferate preceding the onset of recent real-world campaigns and adopt novel adaptive mechanisms to enhance their survival. One of the predictions is that development of large, potentially potent pro-ISIS aggregates can be thwarted by targeting smaller ones.