论文标题
物种丰度分布和物种积累曲线：一般框架和结果
Species Abundance Distribution and Species Accumulation Curve: A General Framework and Results
论文作者
论文摘要
我们建立一个通用框架，该框架在物种丰度分布（SAD）和物种积累曲线（SAC）之间建立了一对一的对应关系。物种的外观速率和每个物种个体的外观时间被建模为泊松过程。物种的数量可以是有限的或无限的。丘陵数量扩展到框架。我们介绍了模型的线性导数比家族，即$ \ mathrm {ldr} _1 $，其中，预期sac的第一个和第二个衍生物的比率是线性函数。提出了D1/D2图来检测数据中的线性模式。通过推断D1/D2图中的曲线，引入了扩展CHAO1估计器的物种丰富度估计值。 $ \ mathrm {ldr} _1 $的悲伤是Engen的扩展负二项式分布，SAC涵盖了几种流行的参数形式，包括Power Law。家庭$ \ mathrm {ldr} _1 $以两种方式扩展：$ \ mathrm {ldr} _2 $允许具有零检测概率的物种和$ \ mathrm {rdr} _1 $，其中派生比是合理的函数。分析实际数据以证明所提出的方法。我们还考虑了仅记录每个物种的几个领先外观时间的情况。我们展示了只有观察到经验囊并阐明其优势比传统曲线拟合方法的优势时，如何进行最大似然推理。
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.
