The Inverse Birthday Problem: An Extension for Estimating Tree Abundance from Occurrence Data

Abstract

The inverse of the classical birthday problem can be applied to estimate the size of a population from occurrence data. However, it generally results in underestimation when used to estimate tree abundance from presence-absence maps. We argue the phenomena arises from the violation of the usual independence and random placement assumptions. This article presents an improved estimator based on a simple paired negative binomial model. In addition, a quadruple negative binomial version of the model is developed, which resolves a controversial issue in the literature. ?The proposed estimator is shown to be asymptotically normally distributed. We examine its performance in a simulation study and by estimating the abundance of several tree species in a permanent forest plot where the actual abundance is known. ?