Defining appropriate null expectations for species distribution hypotheses is important because sampling bias and spatial autocorrelation can produce realistic, but ecologically meaningless, geographic patterns. Generating null species occurrences with similar spatial structure to observed data can help overcome these problems, but existing methods focus on single or pairs of species and do not incorporate between-species spatial structure that may occlude comparative biogeographic analyses. Here, we describe an algorithm for generating randomised species occurrence points that mimic the within- and between-species spatial structure of real datasets and implement it in a new R package - fauxcurrence. The algorithm can be implemented on any geographic domain for any number of species, limited only by computing power. To demonstrate its utility, we apply the algorithm to two common analysis-types: testing the fit of species distribution models (SDMs) and evaluating niche-overlap. The method works well on all tested datasets within reasonable timescales. We found that many SDMs, despite a good fit to the data, were not significantly better than null expectations and identified only two cases (out of a possible 32) of significantly higher niche divergence than expected by chance. The package is user-friendly, flexible and has many potential applications beyond those tested here, such as joint SDM evaluation and species co-occurrence analysis, spanning the areas of ecology, evolutionary biology and biogeography.