物种丰富度空间变异的多重分形模型
A multifractal model for spatial variation in species richness
摘要：
到目前为止，物种-面积关系的模型都集中在平均丰富度作为面积的函数上。我们提出了MFp 1 p2，一个自相似的多重分形。它明确地模拟了丰富度的趋势和变化作为面积的函数，并且是Harte等人（1999）的平均物种丰富度缩放模型的概括。该构造基于矩形的一系列二等分。该模型的两个参数是p1，即出现在较富裕的一半中的物种比例，以及p2，即出现在较贫穷的一半中的物种比例。等效的参数化是a =（p1 + p2）/2和b = p1/p2。这些参数解释如下：a给出平均密度的比例，b给出空间变异的比例。MFp 1 p2的几个属性推导，概括指出，并提出了一些应用。
英文摘要：
Models for species-area relationships up to now have focused on the mean richness as a function of area. We present MFp1p2, a self-similar multifractal. It explicitly models both trend and variation in richness as a function of area, and is a generalisation of the model of scaling of mean species richness due to Harte et al (1999). The construction is based on a cascade of bisections of a rectangle. The two parameters of the model are p1, the proportion of species that occur in the richer half, and p2, the proportion of species that occur in the poorer half. Equivalent parameterisations are a = (p1 + p2)/2 and b = p1/p2. These parameters are interpreted as follows: a gives the scaling of mean density, b gives the scaling of spatial variability. Several properties of MFp1p2 are derived, a generalisation is noted and some applications are suggested.
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