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Ecological entropy is a measure of Biodiversity in the study of biological Ecology .


DEFINITION

Assume that within a system of unlimited individuals, there exists n Species of Organism s (A_1, A_2, ..., A_j, ..., A_n), and the Probability that an individual belongs to species A_j is p_j, where

\sum_{i=1}^n p_i=1


If there are q individuals for each species, the population will be q_1 + q_2 + ... + q_j + ... + q_n. The number of individuals is q^n = n \log q. Set N as constant C.

Diversity within each species, such as male, female, large, small, etc. can be expressed as

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)


Hence the specific diversity can be derived by subtracting the diversities within the species from the diversity of the whole population:

\ C \log q - (C \sum_{j} p_i \log p_i + C \log q) = -C \sum_{j}p_i \log p_i \


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 Bel . The Thermodynamic entropy uses Natural Logarithm (base e), so that the constant C becomes the Boltzmann Constant , the ratio of Universal Gas Constant and Avogadro's Number .


SEE ALSO