# Biodiversity/Introduction
## Definition Biodiversity

Biodiversity, a portmanteau of "bio" (life) and "diversity", generally refers to the variety and variability of life. According to the United Nations Environment Programme (UNEP), biodiversity typically measures variation at the genetic, the species, and the ecosystem level. Biologists most often define biodiversity as the "totality of genes, species and ecosystems of a region". That includes:
* taxonomic diversity (usually measured at the species diversity level)
* ecological diversity often viewed from the perspective of ecosystem diversity
* morphological diversity which stems from genetic diversity and molecular diversity
* functional diversity which is a measure of the number of functionally disparate species within a population (e.g. different feeding mechanism, different motility, predator vs prey, etc.)

## Diversity index

A diversity index is a quantitative measure that reflects how many different types (such as species) there are in a dataset (a community), and simultaneously takes into account how evenly the basic entities (such as individuals) are distributed among those types. The general equation of diversity is often written in the form
    $^{q}\!D=\left({\sum _{i=1}^{R}p_{i}^{q}}\right)^{1/(1-q)}$
and the term inside the parentheses is called the basic sum. Some popular diversity indices correspond to the basic sum as calculated with different values of q.

### Richness

Richness R simply quantifies how many different types the dataset of interest contains. For example, species richness (usually noted S) of a dataset is the number of different species in the corresponding species list. Richness is a simple measure, so it has been a popular diversity index in ecology, where abundance data are often not available for the datasets of interest. Because richness does not take the abundances of the types into account, it is not the same thing as diversity, which does take abundances into account. However, if true diversity is calculated with q = 0, the effective number of types ($^0$D) equals the actual number of types (R).

### Shannon index

The Shannon entropy quantifies the uncertainty (entropy or degree of surprise) associated with this prediction. It is most often calculated as follows:
    $H'=-\sum _{i=1}^{R}p_{i}\ln p_{i}$
where p$_i$ is the proportion of characters belonging to the ith type of letter in the string of interest. In ecology, p$_i$ is often the proportion of individuals belonging to the ith species in the dataset of interest. Then, the Shannon entropy quantifies the uncertainty in predicting the species identity of an individual that is taken at random from the dataset.

### Simpson index

The measure equals the probability that two entities taken at random from the dataset of interest represent the same type. It equals:
    $\lambda =\sum _{i=1}^{R}p_{i}^{2}$,
where R is richness (the total number of types in the dataset). This equation is also equal to the weighted arithmetic mean of the proportional abundances p$_i$ of the types of interest, with the proportional abundances themselves being used as the weights. Proportional abundances are by definition constrained to values between zero and unity, but it is a weighted arithmetic mean, hence λ ≥ 1/R, which is reached when all types are equally abundant.

## Alpha, beta and gamma diversity

In ecology, alpha diversity (α-diversity) is the mean species diversity in sites or habitats at a local scale. The term was introduced by R. H. Whittaker together with the terms beta diversity (β-diversity) and gamma diversity (γ-diversity). Whittaker's idea was that the total species diversity in a landscape (gamma diversity) is determined by two different things, the mean species diversity in sites or habitats at a more local scale (alpha diversity) and the differentiation among those habitats (beta diversity).
* Alpha-Diversity :$^{q}\!D_{\alpha }={\sqrt[{1-q}]{\sum _{j=1}^{N}w_{j}(^{q}\!D_{\alpha j})^{1-q}}}$
* Beta-Diversity :β = γ/α
* Gamma-Diversity :$^{q}\!D_{\gamma }={1 \over {\sqrt[{q-1}]{\sum _{i=1}^{S}p_{i}p_{i}^{q-1}}}}$

## Exercises

* ↑ Biodiversity. (2018, January 7). In Wikipedia, The Free Encyclopedia. Retrieved 17:57, January 10, 2018, from https://en.wikipedia.org/w/index.php?title=Biodiversity&oldid=819113970

## Page information

* Page content is based on: https://en.wikipedia.org/wiki/Biodiversity, https://en.wikipedia.org/wiki/Diversity_index, https://en.wikipedia.org/wiki/Diversity_index, https://en.wikipedia.org/wiki/Alpha_diversity, https://en.wikipedia.org/wiki/Beta_diversity, https://en.wikipedia.org/wiki/Gamma_diversity