Abstract
Assessing species richness (i.e., the number of species in a specific area) is of significant ecological relevance across theoretical, empirical, and practical applications. Accurately estimating species richness remains a persistent statistical challenge, as direct species counts are often unreliable. Consequently, numerous species richness estimation methods have been developed to accommodate a wide range of data types, research goals, assumptions, and sampling designs. The advent of extensive ecological databases and advanced computational capabilities has created new opportunities to apply sequential sampling designs, such as (hierarchically) nested approaches, for more accurate species richness estimation by recording the presence or absence of species over time and space (i.e., across multiple communities or sampling areas). We propose leveraging large-scale datasets by incorporating random effects into non-linear asymptotic functions. In this framework, species richness is treated as a random variable drawn from an estimable distribution. Specifically, we introduce Bayesian hierarchical models in this framework to estimate species richness. We compare our proposed Bayesian models to traditional estimators through simulations and an empirical example of stream fish communities, hierarchically nested within watersheds at the continental scale. The conventional Chao2 performed best, but our findings indicate that Bayesian hierarchical models provide species richness estimates that are comparable in bias and accuracy to traditional estimators, while offering greater precision. However, this gain in precision may come with trade-offs, such as sensitivity to model assumptions or potential biases in certain scenarios.