Species Abundance Distribution and Species Accumulation Curve: A General Framework and Results
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This paper aims at building a general framework that unifies species abundance distribution and species accumulation curve. The framework has two main features. First, the species are modeled as a Poisson process, conditioned on which the individuals are generated by another Poisson process over the time axis. Species-time relationship is explicitly depicted by this doubly stochastic Poisson process. Second, it allows the total number of species to be finite or infinite. As an extreme, we may observe species with zero detection probability. If it happens, there must be an infinite number of such species. Inspired by a diagnostic plot, we propose a special parametric model, where the species abundance distribution is the Engen's extended negative binomial distribution, and the species accumulation curve encompasses some popular families such as the power law and the hyperbola law. The model can be extended to incorporate species with zero detection probability. We also consider stopping rules other than fixing the observation period. Log-likelihood functions under different scenarios are presented.
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