种-面积关系（SAR）：几何方法的模式描述
Species Area Relationship (SAR): Pattern Description with Geometrical Approach
摘要：
有几个公式描述了物种-面积关系的模式，对数-对数线性、半对数线性等。这些模式主要解释了大面积的物种-面积关系，对于小面积，它们提供了与实际数据的显着差异。我们考虑物种个体的几何位置，并在此基础上，我们发现观察到至少一个物种个体的概率。我们应用一个翻译的混合盐水在一个坦克的研究问题来描述SAR的公式。对于一个矩形样区，物种-面积关系遵循以下模式，但有一些简化，即$S=c|A^β+a|^z$，其中$S$是大小为$A$和$a,c,z$的区域中的物种数，$β$是常数，$z<1$和$β\leq1$。我们还展示了如何常数$z$涉及到一些宏观生态模式，即空间聚集，面积覆盖的百分比，和核心卫星模型。我们使用数据的热带树种在巴罗科罗拉多岛（BCI），巴拿马，使用所有的个人从50公顷的阴谋，我们的方法。
英文摘要：
Several formulations are describing the pattern of species-area relationship, log-log linear, semi-log linear, among others. These patterns mainly explain the species-area relationship for large areas, and for the small area, they provide significant differences from real data. We consider the geometric position of individuals of species, and base on that, we find the probability of observing at least one individual of the species. We apply a translation of the well-studied problem of mixed salt-water in a tank to describe the formula of SAR. For a rectangular sample area the species-area relationship follows the pattern, with some simplification, $S=c|A^β+a|^z$, where $S$ is the number of species in the area of size $A$ and $a,c,z$, and $β$ are constants with $z<1$ and $β\leq1$. We also show how the constant $z$ relates to some macroecological patterns, namely spatial aggregation, percentage of area coverage, and the core-satellite model. We exemplify our method using data on tropical tree species from a 50ha plot in Barro Colorado Island (BCI), Panama, using all individuals.
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