Ricotta Carlo
Department of Plant Biology, University of Rome La Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy.
Theor Popul Biol. 2008 Mar;73(2):244-9. doi: 10.1016/j.tpb.2007.10.005. Epub 2007 Nov 24.
Whittaker first proposed to measure the variation in species composition among plots or beta-diversity as the ratio between regional diversity (gamma-diversity) and average local diversity (alpha-diversity). More recently, an alternative way of partitioning diversity for which beta-diversity is obtained as the difference between gamma-diversity and average alpha-diversity has become very popular for linking the structure of species assemblages to ecosystem functioning in a spatially explicit manner. Unfortunately, additive beta-diversity computed from species presences and absences suffers from the major drawback of being dependent on regional species richness. For instance, if the separation between beta-diversity and gamma-diversity is incomplete, so that variation in species composition is affected by species richness, then differences in beta-diversity values among different sets of plots could reflect differences in the species count rather than any fundamental difference in species composition among the plots. Based on the above observation, in this paper I will first propose a basic requirement for beta-diversity measures that adequately captures our intuitive notion of independence of species richness. Next, I will show that additive beta-diversity computed from species presence and absence scores can be interpreted within the framework of fuzzy set theory. Finally, based on this unusual "fuzzy" interpretation of additive beta-diversity, I will introduce two families of parametric beta-diversity measures whose members have varying sensitivities to the presence of rare and frequent species.
惠特克首先提出将样地间物种组成的变化或β多样性衡量为区域多样性（γ多样性）与平均局部多样性（α多样性）的比值。最近，一种划分多样性的替代方法变得非常流行，即通过γ多样性与平均α多样性的差值来获得β多样性，这种方法以空间明确的方式将物种组合结构与生态系统功能联系起来。不幸的是，根据物种的存在与否计算出的加性β多样性存在一个主要缺点，即依赖于区域物种丰富度。例如，如果β多样性和γ多样性之间的区分不完整，以至于物种组成的变化受到物种丰富度的影响，那么不同样地集之间β多样性值的差异可能反映的是物种数量的差异，而不是样地间物种组成的任何根本差异。基于上述观察，在本文中，我将首先提出对β多样性测度的一个基本要求，即它要充分捕捉我们对物种丰富度独立性的直观概念。接下来，我将表明，根据物种存在和缺失分数计算出的加性β多样性可以在模糊集理论的框架内进行解释。最后，基于对加性β多样性这种不同寻常的“模糊”解释，我将引入两类参数化β多样性测度，其成员对稀有和常见物种的存在具有不同的敏感性。
