The Impossibility of Estimating a Negative Binomial Clustering Parameter from Presence-Absence Data: A Comment on He and Gaston

摘要

An important question in ecology is how to infer a species' abundance N from the number of occupied cells m in a land area divided into M uniform grid cells. The question is important because occupancy, or presence-absence, data are easier to collectand thus more available than abundance data. When individual cell abundances are assumed to be independent draws from a negative binomial model, inference about N depends on the value of the clustering parameter k. Clustering concerns variability of abundances across occupied cells, whereas presence-absence data do not reveal cell abundances. Thus, intuition suggests that k cannot be inferred jointly with N but must be specified from outside information. This intuition is verified here for two negativebinomial models used in the literature. The conclusion conflicts with a procedure proposed by He and Gaston (2000) in the American Naturalist.