A New Estimator for the Number of Species in a Population

TL;DR

This paper introduces a novel Bayesian-based estimator for the total number of species in a population, improving flexibility and accuracy over existing methods, with limitations in high variance scenarios.

Contribution

It develops a new estimator by reconciling existing methods and applying a Dirichlet prior, providing simultaneous estimates of multiple parameters in species richness estimation.

Findings

Estimator outperforms existing methods in simulations

Provides simultaneous estimates of T, γ², and λ

Limited in cases where γ² > 1

Abstract

We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by reconciling two estimators of the unobserved probability, and then develop a sequence of improvements culminating in a Dirichlet prior Bayesian reinterpretation of the estimation problem. By means of this, we obtain simultaneous estimates of T, of the normalized interspecies variance $\gamma^2$ and of the parameter $\lambda$ of the prior. Several simulations show that our estimation method is more flexible than several known methods we used as comparison; the only limitation, apparently shared by all other methods, seems to be that it cannot deal with the rare cases in which $\gamma^2 >1$