Accounting for imperfect detection when estimating species-area relationships and beta-diversity

Ecologists have historically quantified fundamental biodiversity patterns, including Species-Area Relationships (SARs) and beta diversity, using observed species counts. However, imperfect detection may often bias derived community metrics and subsequent community models. Although several statistical methods claim to correct for imperfect detection, their performance in species-area and β-diversity research remains unproven. We examine inaccuracies in the estimation of SARs and β-diversity models that emerge from imperfect detection, and whether such errors can be mitigated using a non-parametric diversity estimator (iNEXT.3D) and Multi-Species Occupancy Models (MSOMs). We simulated 23,850 sampling regimes of 2,385 fragmented communities, varying the mean and standard deviation of species detection probabilities, and the number of sampling repetitions. We then quantified the bias, accuracy, and precision of derived estimates of model coefficients for SARs and the effects of patch area on β-diversity (pairwise Sørensen similarity). Imperfect detection biased estimates of all evaluated parameters, particularly when mean detection probabilities were low and there were few sampling repetitions. Observed counts consistently underestimated species richness and SAR z-values, and overestimated SAR c-values; iNEXT.3D and MSOMs only partially resolved these biases. iNEXT.3D provided the best estimates of SAR z-values, although MSOM estimates were generally comparable. All three methods accurately estimated pairwise Sørensen similarity in most circumstances, but only MSOMs provided unbiased estimates of the coefficients of models examining covariate effects on β-diversity. Even when using iNEXT.3D or MSOMs, imperfect detection consistently caused inaccuracies in SAR coefficient estimates, calling into question the robustness of previous SAR studies. Furthermore, the inability of observed counts and iNEXT.3D to estimate β-diversity model coefficients resulted from a systematic, area-related bias in Sørensen similarity estimates. Importantly, MSOMs corrected for these biases in β-diversity assessments, even in suboptimal scenarios. Nonetheless, as estimator performance consistently improved with increasing sampling repetitions, the importance of appropriate sampling effort cannot be understated.