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Species with highest absolute entropy2/29/2024 They are especially prominent in economics, where they (or their inverses or complements) are used to measure such things as the concentration of wealth among individuals or the concentration of industrial capacity among corporations. Measures which behave like this are important in many disciplines that deal with complex systems. Then diversity would drop continuously as species headed towards extinction. For a given number of species, the maximum possible diversity should occur when all species are equally common, and the minimum possible diversity should occur when all but one of the species were vanishingly rare. Biologists needed to expand their diversity concept to account for abundances when needed. A simple presence-or-absence species count does not capture this difference. It matters how the individuals are distributed among the species. A ten-species butterfly community with one abundant species and nine vanishingly rare ones is, in many ecological aspects, more similar to a butterfly community with only one species than to a butterfly community with ten equally common species. An oak forest with a few pine trees is very different from a pine forest with a few oak trees. However, there are many applications in which a simple species count is not sufficient. For example, it is very useful when prioritizing areas for conservation. In spite of the difficulty of its estimation, species richness is still an important biological community parameter for many theoretical and practical purposes. Using statistical tools based on Alan Turing’s WWII codebreaking efforts for the British, Anne Chao developed an estimator for a lower bound on the total number of species in a community ( Chao, 1984), but the actual total number of species cannot be estimated without bias. In such places, the species count depends strongly on the sampling effort and also on the distribution of abundance across species. Even at the end of those ten years of intense collecting, they were still adding species they had never before collected, and this is typical of tropical ecosystems. For example, Phil DeVries, Tom Walla, and Harold Greeney collected butterflies at a single site in the Amazon rainforest for ten years ( DeVries & Walla, 2001). In practice, however, it is almost impossible to accurately count the number of species in rich communities, where most of the species are typically rare. At first glance this kind of diversity seems to be conceptually simple to interpret, and it undoubtedly captures an important quality of an ecosystem. When biologists first started talking about diversity, they simply meant the number of species in a community, the so-called «species richness». Instead of establishing a definition of diversity by fiat, biology has gradually been evolving a dynamic diversity concept that addresses a growing number of novel theoretical and practical demands. We could achieve precision of meaning by simply defining diversity in a certain way, but that is a cheap solution there would be no guarantee that diversity so defined would connect in a deep way to future theories. This kind of issue is always a challenging one for a young science. In spite of its importance in biology, however, there has been little agreement on what it really means or how it should be quantified. It is one of the fundamental concepts of biology, particularly its sub-disciplines ecology, evolutionary theory, and genetics, but the same concept or a close analogue plays an important role in economics, information theory, and physics, among others. Keywords: diversity, effective number of species, Shannon entropy, species richness.ĭiversity is both a common buzzword in daily life and a precise scientific concept that arises in many different disciplines. The effective number of species, then, seems to capture most (though not all) of what biologists mean by diversity. Biologists now usually transform the traditional measures to the «effective number of species», whose mathematics does support most of the rules of inference that biologists apply to them. Biological reasoning about diversity often implicitly assumed that measures of diversity had certain mathematical properties, but most of biology’s traditional diversity measures did not actually possess these properties, a situation which often led to mathematically and biologically invalid inferences. In the course of this evolution, diversity measures have often been borrowed from other disciplines. The concept of biological diversity has evolved from a simple count of species to more sophisticated measures that are sensitive to relative abundances and even to evolutionary divergence times between species.
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