Estimation of Species Richness: Mixture Models, the Role of Rare Species, and Inferential Challenges

We examine the role of rare species in the problem of estimating within-habitat species richness based on sampling data. Richness estimation can be modeled realistically for abundance-based and incidence-based data using Poisson or binomial mixtures, respectively. The problem can be reduced to estimation of the odds of the probability of a species remaining undetected in the sample or sample set. Within this rigorous statistical framework, we explore existing methods of richness estimation and assess their limitations. We do this by modeling the addition of increasing numbers of rare, undetected species to a reference assemblage, assessing the power of different methods to distinguish the modified species assemblages from the reference assemblage. (We use empirical example data sets for birds, seeds, and beetles as reference assemblages.) By considering the contributions of rare species and the role of undetected species for a fixed sampling effort, we show why the problem of richness estimation is so difficult, and we discuss what statistical models can provide.