Risk of biological invasion is not uniformly distributed in space. To identify hot spots of invasion, researchers increasingly use models to identify the boundaries of an organism's niche. Models are estimated and projected onto a map for visualization and analysis. Conventional methods for ecological niche identification are beset by numerous, well-known problems: the boundaries of ecological niches are complex and not well represented by simple regression methods; observations of individual fitness are rare so surrogate measurements must be used, for instance records of sightings, but using only observations of species occurrence precludes classification approaches like logistic regression; measurements can rarely be confirmed to be statistically independent, particularly spatial autocorrelation is pervasive. These obstacles introduce bias and false precision when inappropriate models are used to estimate niche boundaries. Proposals to counter these obstacles vary in effectiveness and transparency. I propose that a useful method for ecological niche identification should adopt flexible computational routines for estimating the support or tail quantiles of a statistical distribution. The flexibility of the computational method (e.g., a neural network) counters the complexity of the niche boundary. By estimating the distribution support one might skirt the problem of independence if the range of the distribution is well represented by the data. In some cases a nonparametric bootstrap is justified and can be used to estimate confidence sets. Estimates of uncertainty are crucial if risk maps are used for hypothesis testing or to inform policy. As examples, I apply these methods to map invasion risk for zebra mussels (Dreissena polymorpha) in North America and potential distribution of African malaria mosquitoes (Anopheles spp.) in Africa under post-climate change scenarios. In both cases I find that pervasive model uncertainty precludes making precise forecasts of future species distributions. Analyses which do not estimate uncertainty may be misleadingly precise.