Accurate estimates of species richness are necessary to test predictions of ecological theory and evaluate biodiversity for conservation purposes. However, species richness is difficult to measure in the field because some species will almost always be overlooked due to their cryptic nature or the observer's failure to perceive their cues. Common measures of species richness that assume consistent observability across species are inviting because they may require only single counts of species at survey sites. Single-visit estimation methods ignore spatial and temporal variation in species detection probabilities related to survey or site conditions that may confound estimates of species richness. We used simulated and empirical data to evaluate the bias and precision of raw species counts, the limiting forms of jackknife and Chao estimators, and multi-species occupancy models when estimating species richness to evaluate whether the choice of estimator can affect inferences about the relationships between environmental conditions and community size under variable detection processes. Four simulated scenarios with realistic and variable detection processes were considered. Results of simulations indicated that (1) raw species counts were always biased low, (2) single-visit jackknife and Chao estimators were significantly biased regardless of detection process, (3) multispecies occupancy models were more precise and generally less biased than the jackknife and Chao estimators, and (4) spatial heterogeneity resulting from the effects of a site covariate on species detection probabilities had significant impacts on the inferred relationships between species richness and a spatially explicit environmental condition. For a real dataset of bird observations in northwestern Alaska, the four estimation methods produced different estimates of local species richness, which severely affected inferences about the effects of shrubs on local avian richness. Overall, our results indicate that neglecting the effects of site covariates on species detection probabilities may lead to significant bias in estimation of species richness, as well as the inferred relationships between community size and environmental covariates.