Understanding the interactions between the Earth's microbiome and the physical, chemical and biological environment is a fundamental goal of microbial ecology. We describe a bioclimatic modeling approach that leverages artificial neural networks to predict microbial community structure as a function of environmental parameters and microbial interactions. This method was better at predicting observed community structure than were any of several single-species models that do not incorporate biotic interactions. The model was used to interpolate and extrapolate community structure over time with an average Bray-Curtis similarity of 89.7. Additionally, community structure was extrapolated geographically to create the first microbial map derived from single-point observations. This method can be generalized to the many microbial ecosystems for which detailed taxonomic data are currently being generated, providing an observation-based modeling technique for predicting microbial taxonomic structure in ecological studies.