Several non-parametric estimators have been proposed for estimating species richness from a spatial sample. While the label non-parametric may suggest that a method makes few assumptions, these estimators are known to rely on a homogeneous community with certain abundance distributions. In this paper we simulate the effect of different abundance distributions (geometric series, log-normal, and broken-stick models) and of different types of spatial heterogeneity (species-specific aggregation, gradients, and an edge effect) on the performance of four non-parametric estimators of species richness for presence-absence data (Jack1, Jack2, Chao2, and ICE). In order to focus on parameter settings likely to be encountered in real communities, we derived simulation parameters from real data from four agricultural habitat types in central Switzerland. Based on an ANOVA of relative bias, all estimators failed for communities simulated under the geometric model and were considerably affected by a simulated edge effect, but species-specific aggregation, an environmental gradient, and differences between community types had little effect on estimator performance. Species abundance distribution and spatial heterogeneity influence estimator performance by decreasing the proportion of species represented in the sample, which may be counteracted by adapting the sampling design. For reasonably complete samples, Chao2 was the least biased, but suffered from a large variance, as did Jack2. We recommend using the first order jackknife Jack1 or the incidence-based coverage estimator ICE, but only for samples that contain at least 80% of the species.