物种绝对分布和物种积累曲线：一个一般框架和结果
Species Abundance Distribution and Species Accumulation Curve: A General Framework and Results
摘要：
我们建立了一个一般的框架，建立了一个一对一的对应关系之间的物种多度分布（SAD）和物种积累曲线（SAC）。物种的出现率和每个物种的个体的出现时间被建模为泊松过程。物种的数量可以是有限的，也可以是无限的。将Hill数推广到框架中。我们引入了一个线性导数比率模型族，$\mathrm{LDR}_1$，其中期望SAC的一阶和二阶导数的比率是线性函数。提出了一种D1/D2图来检测数据中的这种线性模式。通过对D1/D2样地中的曲线进行外推，得到了一个物种丰富度估计，它是Chao 1估计的推广。$\mathrm{LDR}_1$的SAD是Engen的扩展负二项分布，SAC包括几种流行的参数形式，包括幂律。家族$\mathrm{LDR}_1$以两种方式扩展：$\mathrm{LDR}_2$，其允许具有零检测概率的物种;以及$\mathrm{RDR}_1$，其中导数比率是有理函数。实际数据进行了分析，以证明所提出的方法。我们还考虑的情况下，我们只记录了几个领先的出现时间的每个物种。我们展示了如何极大似然推理时，只有经验SAC观察，并阐明其优势，传统的曲线拟合方法。
英文摘要：
We build a general framework which establishes a one-to-one correspondence between species abundance distribution (SAD) and species accumulation curve (SAC). The appearance rates of the species and the appearance times of individuals of each species are modeled as Poisson processes. The number of species can be finite or infinite. Hill numbers are extended to the framework. We introduce a linear derivative ratio family of models, $\mathrm{LDR}_1$, of which the ratio of the first and the second derivatives of the expected SAC is a linear function. A D1/D2 plot is proposed to detect this linear pattern in the data. By extrapolation of the curve in the D1/D2 plot, a species richness estimator that extends Chao1 estimator is introduced. The SAD of $\mathrm{LDR}_1$ is the Engen's extended negative binomial distribution, and the SAC encompasses several popular parametric forms including the power law. Family $\mathrm{LDR}_1$ is extended in two ways: $\mathrm{LDR}_2$ which allows species with zero detection probability, and $\mathrm{RDR}_1$ where the derivative ratio is a rational function. Real data are analyzed to demonstrate the proposed methods. We also consider the scenario where we record only a few leading appearance times of each species. We show how maximum likelihood inference can be performed when only the empirical SAC is observed, and elucidate its advantages over the traditional curve-fitting method.
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