Entropy (ecology)
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201641903
2008-03-28T19:12:49Z
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{{Mergeto|Shannon index|date=March 2008}}
'''Ecological entropy''' is a measure of [[biodiversity]] in the study of biological [[ecology]].
==Definition==
Assume that within a system of unlimited individuals, there exists <math>n</math> [[species]] of [[organism]]s (<math>A_1, A_2, ..., A_j, ..., A_n</math>), and the [[probability]] that an individual belongs to species <math>A_j</math> is <math>p_j</math>, where
:<math>\sum_{i=1}^n p_i=1</math>
If there are <math>q</math> individuals for each species, the population will be <math>q_1 + q_2 + ... + q_j + ... + q_n</math>. The number of individuals is <math>q^n = n \log q</math>. Set <math>N</math> as constant <math>C</math>.
Diversity within each species, such as male, female, large, small, etc. can be expressed as
:<math>C \sum_{j} p_i \log q_j = C \sum_{j}p_i \log p_I + C \log q \quad (\mbox{since }q_j = qp_I)</math>
Hence the specific diversity can be derived by subtracting the diversities within the species from the diversity of the whole population:
:<math>\ C \log q - (C \sum_{j} p_i \log p_i + C \log q) = -C \sum_{j}p_i \log p_i \ </math>
The expression is the same as that of [[information]] entropy, except that it is customary to use [[binary logarithm]] (base 2) for information entropy, the unit being [[bit]], and to use [[common logarithm]] (base 10) for ecological entropy, the unit being [[decibel|bel]]. The [[thermodynamic]] entropy uses [[natural logarithm]] (base <math>e</math>), so that the constant <math>C</math> becomes the [[Boltzmann constant]], the ratio of [[universal gas constant]] and [[Avogadro's number]].
==See also==
*[[Entropy]] (thermodynamics)
*[[Entropy (information theory)]]
[[Category:Measurement of biodiversity]]
[[Category:Entropy and information]]
[[zh:熵 (生态学)]]