Species diversity is the number of different
species
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
that are represented in a given
community
A community is a social unit (a group of living things) with commonality such as place, norms, religion, values, customs, or identity. Communities may share a sense of place situated in a given geographical area (e.g. a country, village, tow ...
(a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant). Meanings of species diversity may include
species richness
Species richness is the number of different species represented in an ecological community, landscape or region. Species richness is simply a count of species, and it does not take into account the abundances of the species or their relative a ...
, taxonomic or phylogenetic diversity, and/or
species evenness Species evenness refers to how close in numbers each species in an environment is. Mathematically it is defined as a diversity index, a measure of biodiversity which quantifies how equal the community is numerically. So if there are 40 foxes and 100 ...
. Species richness is a simple count of species. Taxonomic or phylogenetic diversity is the genetic relationship between different groups of species. Species evenness quantifies how equal the
abundances of the species are.
[Hill, M. O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432][Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography, 33, 2-22. ][Tuomisto, H. 2010. A consistent terminology for quantifying species diversity? Yes, it does exist. Oecologia 4: 853–860. ]
Calculation of diversity
Species diversity in a dataset can be calculated by first taking the
weighted average
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...
of species proportional abundances in the dataset, and then taking the
inverse of this. The equation is:
:
The
denominator
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
equals mean proportional species abundance in the dataset as calculated with the weighted
generalized mean
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means).
De ...
with exponent ''q'' - 1. In the equation, ''S'' is the total number of species (species richness) in the dataset, and the proportional abundance of the ''i''th species is
. The proportional abundances themselves are used as weights.
The equation is often written in the equivalent form:
:
The value of ''q'' determines which mean is used. ''q'' = 0 corresponds to the weighted
harmonic mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired.
The harmonic mean can be expressed as the recipro ...
, which is 1/''S'' because the
values cancel out, with the result that
''0''''D'' is equal to the number of species or species richness, ''S''. ''q'' = 1 is undefined, except that the limit as ''q'' approaches 1 is well defined:
[Xu, S., Böttcher, L., and Chou, T. (2020). Diversity in biology: definitions, quantification and models. Physical Biology, 17, 031001. ]
:
which is the exponential of the
Shannon entropy
Shannon may refer to:
People
* Shannon (given name)
* Shannon (surname)
* Shannon (American singer), stage name of singer Shannon Brenda Greene (born 1958)
* Shannon (South Korean singer), British-South Korean singer and actress Shannon Arrum Wi ...
.
''q'' = 2 corresponds to the
arithmetic mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...
. As ''q'' approaches
infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions amo ...
, the generalized mean approaches the maximum
value. In practice, ''q'' modifies species weighting, such that increasing ''q'' increases the weight given to the most abundant species, and fewer equally abundant species are hence needed to reach mean proportional abundance. Consequently, large values of ''q'' lead to smaller species diversity than small values of ''q'' for the same dataset. If all species are equally abundant in the dataset, changing the value of ''q'' has no effect, but species diversity at any value of ''q'' equals species richness.
Negative values of ''q'' are not used, because then the effective number of species (diversity) would exceed the actual number of species (richness). As ''q'' approaches negative infinity, the generalized mean approaches the minimum
value. In many real datasets, the least abundant species is represented by a single individual, and then the effective number of species would equal the number of individuals in the dataset.
The same equation can be used to calculate the diversity in relation to any classification, not only species. If the individuals are classified into genera or functional types,
represents the proportional abundance of the ''i''th genus or functional type, and
''q''''D'' equals genus diversity or functional type diversity, respectively.
Diversity indices
Often researchers have used the values given by one or more diversity indices to quantify species diversity. Such indices include
species richness
Species richness is the number of different species represented in an ecological community, landscape or region. Species richness is simply a count of species, and it does not take into account the abundances of the species or their relative a ...
, the
Shannon 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 that can simultaneously take into account the phylogenetic relations among the individuals distributed a ...
, the
Simpson index, and the complement of the Simpson index (also known as the Gini-Simpson index).
[Jost, L. (2006) Entropy and diversity. Oikos, 113, 363–375]
When interpreted in ecological terms, each one of these indices corresponds to a different thing, and their values are therefore not directly comparable. Species richness quantifies the actual rather than effective number of species. The Shannon index equals log(
''1''''D''), that is, q approaching 1, and in practice quantifies the uncertainty in the species identity of an individual that is taken at random from the dataset. The Simpson index equals 1/
''2''''D'', q = 2, and quantifies the probability that two individuals taken at random from the dataset (with replacement of the first individual before taking the second) represent the same species. The Gini-Simpson index equals 1 - 1/
''2''''D'' and quantifies the probability that the two randomly taken individuals represent different species.
Sampling considerations
Depending on the purposes of quantifying species diversity, the data set used for the calculations can be obtained in different ways. Although species diversity can be calculated for any data-set where individuals have been identified to species, meaningful ecological interpretations require that the dataset is appropriate for the questions at hand. In practice, the interest is usually in the species diversity of areas so large that not all individuals in them can be observed and identified to species, but a sample of the relevant individuals has to be obtained. Extrapolation from the sample to the underlying population of interest is not straightforward, because the species diversity of the available sample generally gives an underestimation of the species diversity in the entire population. Applying different
sampling methods
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt ...
will lead to different sets of individuals being observed for the same area of interest, and the species diversity of each set may be different. When a new individual is added to a dataset, it may introduce a species that was not yet represented. How much this increases species diversity depends on the value of ''q'': when ''q'' = 0, each new actual species causes species diversity to increase by one effective species, but when ''q'' is large, adding a rare species to a dataset has little effect on its species diversity.
In general, sets with many individuals can be expected to have higher species diversity than sets with fewer individuals. When species diversity values are compared among sets, sampling efforts need to be standardised in an appropriate way for the comparisons to yield ecologically meaningful results.
Resampling methods can be used to bring samples of different sizes to a common footing.
Species discovery curve In ecology, the species discovery curve (also known as a species accumulation curve or collector's curve) is a graph recording the cumulative number of species of living things recorded in a particular environment as a function of the cumulative eff ...
s and the number of species only represented by one or a few individuals can be used to help in estimating how representative the available sample is of the population from which it was drawn.
[ Chao, A. (2005) Species richness estimation. Pages 7909-7916 in N. Balakrishnan, C. B. Read, and B. Vidakovic, eds. Encyclopedia of Statistical Sciences. New York, Wiley.]
Trends
The observed species diversity is affected not only by the number of individuals but also by the heterogeneity of the sample. If individuals are drawn from different environmental conditions (or different
habitat
In ecology, the term habitat summarises the array of resources, physical and biotic factors that are present in an area, such as to support the survival and reproduction of a particular species. A species habitat can be seen as the physical ...
s), the species diversity of the resulting set can be expected to be higher than if all individuals are drawn from a similar environment. Increasing the area sampled increases observed species diversity both because more individuals get included in the sample and because large areas are environmentally more heterogeneous than small areas.
See also
*
Alpha diversity
In ecology, alpha diversity (α-diversity) is the mean species diversity in a site at a local scale. The term was introduced by R. H. WhittakerWhittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monograp ...
*
Beta diversity
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bÄ“Ì‚ta or ell, βήτα, vÃta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiod ...
*
Biodiversity
Biodiversity or biological diversity is the variety and variability of life on Earth. Biodiversity is a measure of variation at the genetic (''genetic variability''), species (''species diversity''), and ecosystem (''ecosystem diversity'') l ...
**
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 that can simultaneously take into account the phylogenetic relations among the individuals distributed a ...
**
Measurement of biodiversity
Conservation biologists have designed a variety of objective means to measure biodiversity empirically. Each measure of biodiversity relates to a particular use of the data. For practical conservationists, measurements should include . For othe ...
*
Coexistence theory
Coexistence theory is a framework to understand how competitor traits can maintain species diversity and stave-off competitive exclusion even among similar species living in ecologically similar environments. Coexistence theory explains the st ...
*
Dark diversity
Dark diversity is the set of species that are absent from a study site but present in the surrounding region and potentially able to inhabit particular ecological conditions. It can be determined based on species distribution, dispersal potential a ...
*
Gamma diversity
In ecology, gamma diversity (γ-diversity) is the total species diversity in a landscape. The term was introduced by R. H. WhittakerWhittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279â ...
*
Genetic diversity
Genetic diversity is the total number of genetic characteristics in the genetic makeup of a species, it ranges widely from the number of species to differences within species and can be attributed to the span of survival for a species. It is dis ...
*
Latitudinal gradients in species diversity
Species richness, or biodiversity, increases from the poles to the tropics for a wide variety of terrestrial and marine organisms, often referred to as the latitudinal diversity gradient. The latitudinal diversity gradient is one of the most widel ...
*
Relative species abundance Relative species abundance is a component of biodiversity and is a measure of how common or rare a species is relative to other species in a defined location or community.Hubbell, S. P. 2001. ''The unified neutral theory of biodiversity and biogeogr ...
*
Species–area relationship
The species-area relationship or species-area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and e ...
Notes
External links
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Ecological metrics
Habitat
Environmental terminology
Measurement of biodiversity