Maximizing Diversity in Biology and Beyond
Maximizing Diversity in Biology and Beyond
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DOI：
10.3390/e18030088
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发表时间：
2016-03-01
期刊：
影响因子：
2.7
通讯作者：
Meckes, Mark W.
中科院分区：
文献类型：
--
作者：
Leinster, Tom;Meckes, Mark W.
熵有多种名称，长期以来一直被用作生态学以及遗传学、经济学和其他领域多样性的衡量标准。关于多样性有一系列的观点，以实数参数 q 为索引，对稀有物种给予不同程度的重视。 Leinster 和 Cobbold (2012) 提出了一种单参数多样性衡量标准，同时考虑了这种变异和物种之间不同的相似性。由于后一个特征，物种的均匀分布并没有使多样性最大化。因此很自然地会问：哪些分布最大化了多样性，其最大值是多少？原则上，两个答案都取决于 q，但我们的主要定理是两者都不取决于。因此，存在一个单一的分布，可以同时从所有角度最大化多样性，并且任何物种列表都具有明确的最大多样性值。此外，可以在有限时间内计算最大化分布，并且从某个特定观点 q > p 最大化多样性的任何分布实际上最大化了所有 q 的多样性。尽管我们用生态术语来表达我们的结果，但它们的应用非常广泛，在图论和度量几何中都有应用。
Entropy, under a variety of names, has long been used as a measure of diversity in ecology, as well as in genetics, economics and other fields. There is a spectrum of viewpoints on diversity, indexed by a real parameter q giving greater or lesser importance to rare species. Leinster and Cobbold (2012) proposed a one-parameter family of diversity measures taking into account both this variation and the varying similarities between species. Because of this latter feature, diversity is not maximized by the uniform distribution on species. So it is natural to ask: which distributions maximize diversity, and what is its maximum value? In principle, both answers depend on q, but our main theorem is that neither does. Thus, there is a single distribution that maximizes diversity from all viewpoints simultaneously, and any list of species has an unambiguous maximum diversity value. Furthermore, the maximizing distribution(s) can be computed in finite time, and any distribution maximizing diversity from some particular viewpoint q > p actually maximizes diversity for all q. Although we phrase our results in ecological terms, they apply very widely, with applications in graph theory and metric geometry.