Modelling species abundance using the Poisson-Tweedie family

TLDR

Species distributions often deviate from randomness due to ecological factors, leading to over‑dispersion, zero‑inflation, and heavy tails that are commonly modeled with negative binomial, Poisson‑inverse Gaussian, or zero‑inflated Poisson distributions instead of the Poisson. The study proposes a three‑parameter discrete distribution that unifies Poisson, NB, PIG, Neyman Type A, and Poisson‑Pascal models. The authors develop a three‑parameter Poisson‑Tweedie family that spans tail behaviours beyond the negative binomial and apply it to grouped counts of Lake Erie coliform bacteria and European corn borer larvae, using likelihood‑based inference. The model shows capacity to accommodate zero‑inflated data. © 2010 John Wiley & Sons, Ltd.

Abstract

The distribution of an organism species in the environment deviates frequently from randomness due to natural cycles, availability of food resources and avoidance of harm. As a result, observed data can show over-dispersion, zero-inflation and even heavy tail. Models such as the negative binomial (NB), Poisson-inverse Gaussian (PIG), and zero-inflated Poisson are frequently used in applications instead of the Poisson distribution which is usually the default model. This paper uses a three-parameter discrete distribution that unifies distributions such as Poisson, NB, PIG, Neyman Type A, and Poisson-Pascal. The three-parameter family covers a wide range of tail heaviness relative to NB, and thus suitable for modelling over-dispersed count data with a shorter or longer tail. Moreover, it shows some capacity for zero-inflated data. Grouped counts of coliform bacteria from Lake Erie and counts of European corn borer larvae in field corn are used to illustrate the application of the model and the associated likelihood-based inferences. Copyright © 2010 John Wiley & Sons, Ltd.