Multiple stable states, bifurcations and thresholds are fashionable concepts in the ecological literature, a recognition that complex ecosystems may at times exhibit the interesting dynamic behaviours predicted by relatively simple biomathematical models. Recently, several papers in Global Ecology and Biogeography, Proceedings of the National Academy of Sciences USA, Science and elsewhere have attempted to quantify the prevalence of alternate stable states in the savannas of Africa, Australia and South America, and the tundra–taiga–grassland transitions of the circum-boreal region using satellite-derived woody canopy cover. While we agree with the logic that basins of attraction can be inferred from the relative frequencies of ecosystem states observed in space and time, we caution that the statistical methodologies underlying the satellite product used in these studies may confound our ability to infer the presence of multiple stable states. We demonstrate this point using a uniformly distributed ‘pseudo-tree cover’ database for Africa that we use to retrace the steps involved in creation of the satellite tree-cover product and subsequent analysis. We show how classification and regression tree (CART)-based products may impose discontinuities in satellite tree-cover estimates even when such discontinuities are not present in reality. As regional and global remote sensing and geospatial data become more easily accessible for ecological studies, we recommend careful consideration of how error distributions in remote sensing products may interact with the data needs and theoretical expectations of the ecological process under study.