Maximum-likelihood estimation of the geometric niche preemption model

The 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.