Entropy (ecology) - Citizendia

Ecological entropy is a measure of biodiversity in the study of biological ecology. Biodiversity is the variation of Life forms within a given Ecosystem, Biome or for the entire Earth. Ecology (from Greek grc οἶκος oikos, "house(hold" and grc -λογία -logia) is the scientific study of

Definition

Assume that within a system of unlimited individuals, there exists $n$ species of organisms ( $A 1, A 2,. In Biology, a species is one of the basic units of Biological classification and a Taxonomic rank. . . , A j,. . . , A n$ ), 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 $q 1 + q 2 + . Probability is the likelihood or chance that something is the case or will happen . . + q j + . . . + q n$ . 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. Information as a concept has a diversity of meanings from everyday usage to technical settings In Mathematics, the binary logarithm (log2 n) is the Logarithm for Base 2 A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication The common logarithm is the Logarithm with base 10 It is also known as the decadic logarithm, named after its base The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to 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. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " The natural logarithm, formerly known as the Hyperbolic logarithm is the Logarithm to the base e, where e is an irrational Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working The Avogadro constant (symbols L, N A also called Avogadro's number, is the number of "elementary entities" (usually Atoms

Definition

See also