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Abstract
AbstractThe geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May's equation. This article proposes a maximum‐likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum‐likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum‐likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.
Highlights
The statistical modeling of the relative abundance of a set of species in an ecological community has a longstanding history (Wilson, 1991)
In this article we focus on the geometric series, known as the niche preemption hypothesis
We study the statistical properties of the new maximum likelihood (ML) estimator and its classical counterparts in a simulation study in the Monte Carlo simulation Section below
Summary
Open Research Statement: Data sets utilized for this research were taken from the literature and are publicly available:. The Australian Bird data is available in printed form in the article of Fattorini (2005; Appendix 2) and as a data object in the R package MLpreemption. The Indian Dung beetles data is available in printed form in the book of Magurran (2004) and as a data object in the R package MLpreemption. This article proposes a maximum likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. We obtain the distribution of the maximum likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples.
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