An Integrated Framework for Estimating the Number of Classes with Application for Species Estimation

Abstract

The two most common approaches for estimating the number of distinct classes within a population are either to use sampling data directly with combinatorial arguments or to extrapolate historical discovery data. However, in the former case, such detailed sampling data is often unavailable, while the latter approach makes assumptions on the form of parametric curves used to fit the discovery data, that are often lacking in theoretical justification. Instead, we propose an integrated transdisciplinary framework that dissolves the boundaries between the above two approaches. This is achieved by directly describing the sampling discovery process in parallel with describing a co-variate latent effort process, where we have historical discovery data for the former process and some proxy data for the latent process. The linkage between these two processes allows one to form data on sampling records by forcing some constraints on how many samples were taken over time. Due to the nature of the constrained data, many inference techniques become infeasible. However, simulation-based methods such as Approximate Bayesian Computation remain available. Our proposed approach is demonstrated and analysed through many simulation experiments, and finally applied in the ecology field to estimate the number of species as an example of the number of classes problem.