The decline of species in natural habitats concerns ecologists, who view extinction as a danger and conservation of biological diversity as a goal. In contrast, the proliferation of ‘undesirable’ species is the principal concern of epidemiologists, who view persistence as a problem and eradication as an achievement. While ecologists and epidemiologists have essentially opposite goals, the mathematical structure of the population dynamics that they study is very similar. We briefly review the similarities and differences between these two fields, emphasizing recent work in both areas on the effects of spatial synchrony and dynamical chaos. We hope to stimulate further cross–fertilization of ideas between the disciplines.