Nonparametric species richness estimation under convexity constraint

TL;DR

This paper introduces a nonparametric method for estimating total species richness using convexity constraints on abundance distributions, providing new estimators and confidence intervals with demonstrated effectiveness.

Contribution

It proposes a novel convexity-constrained estimation approach for species richness, including new estimators and bootstrap-based confidence intervals.

Findings

Estimators perform well in simulations.

Method provides reliable confidence intervals.

Application to real data demonstrates practical utility.

Abstract

We consider the estimation of the total number $N$ of species based on the abundances of species that have been observed. We adopt a non parametric approach where the true abundance distribution $p$ is only supposed to be convex. From this assumption, we propose a definition for convex abundance distributions. We use a least-squares estimate of the truncated version of $p$ under the convexity constraint. We deduce two estimators of the total number of species, the asymptotic distribution of which are derived. We propose three different procedures, including a bootstrap one, to obtain a confidence interval for $N$. The performances of the estimators are assessed in a simulation study and compared with competitors. The proposed method is illustrated on several examples.