In
ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overl ...
, alpha diversity (α-diversity) is the mean
species diversity
Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundan ...
in a site at a local scale. The term was introduced by
R. H. Whittaker[Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338. ][Whittaker, R. H. (1972). Evolution and Measurement of Species Diversity. Taxon, 21, 213-251. ] together with the terms
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 ...
(β-diversity) and
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 ...
(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 at a more local scale (alpha diversity) and the differentiation among those sites (
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 ...
).
Scale considerations
Both the area or
landscape
A landscape is the visible features of an area of land, its landforms, and how they integrate with natural or man-made features, often considered in terms of their aesthetic appeal.''New Oxford American Dictionary''. A landscape includes the ...
of interest and the sites within it may be of very different sizes in different situations, and no consensus has been reached on what
spatial scales
Spatial scale is a specific application of the term scale for describing or categorizing (e.g. into orders of magnitude) the size of a space (hence ''spatial''), or the extent of it at which a phenomenon or process occurs.
For instance, in phy ...
are appropriate to quantify alpha diversity. It has therefore been proposed that the definition of alpha diversity does not need to be tied to a specific spatial scale: alpha diversity can be measured for an existing dataset that consists of subunits at any scale.
[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. ] The subunits can be, for example, sampling units that were already used in the field when carrying out the
inventory
Inventory (American English) or stock (British English) refers to the goods and materials that a business holds for the ultimate goal of resale, production or utilisation.
Inventory management is a discipline primarily about specifying the shap ...
, or grid cells that are delimited just for the purpose of analysis. If results are extrapolated beyond the actual observations, it needs to be taken into account that the
species diversity
Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundan ...
in the subunits generally gives an underestimation of the species diversity in larger areas.
Different concepts
Ecologists have used several slightly different definitions of alpha diversity. Whittaker himself used the term both for the species diversity in a single subunit and for the mean species diversity in a collection of subunits.
[Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338. ][Whittaker, R. H. (1972). Evolution and Measurement of Species Diversity. Taxon, 21, 213-251. ] It has been argued that defining alpha diversity as a mean across all relevant subunits is preferable, because it agrees better with Whittaker's idea that total species diversity consists of alpha and beta components.
[Tuomisto, H. (2011) Commentary: do we have a consistent terminology for species diversity? Yes, if we choose to use it. Oecologia, 167, 903-911.]
Definitions of alpha diversity can also differ in what they assume
species diversity
Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundan ...
to be. Often researchers use the values given by one or more
diversity indices, such as
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 ...
(which is simply a count of species), 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 ...
or the
Simpson index (which take into account also species proportional abundances).
However, it has been argued that it would be better to use the
effective number of species as the universal measure of species diversity. This measure allows weighting rare and abundant species in different ways, just as the diversity indices collectively do, but its meaning is intuitively easier to understand. The effective number of species is 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).
[Jost, L. (2006) Entropy and diversity. Oikos, 113, 363–375][Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427–2439.][Tuomisto, H. 2010. A consistent terminology for quantifying species diversity? Yes, it does exist. Oecologia 4: 853–860. ]
Calculation
Suppose species diversity is equated with the effective number of species, and alpha diversity with the mean species diversity per subunit. Then alpha diversity can be calculated in two different ways that give the same result. The first approach is to calculate a 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 ...
of the within-subunit species proportional abundances, and then take the inverse of this mean. The second approach is to calculate the species diversity for each subunit separately, and then take a weighted generalized mean of these.
If the first approach is used, the equation is:
:
In the equation, ''N'' is the total number of subunits and ''S'' is the total number of species (species richness) in the dataset. The proportional abundance of the ''i''th species in the ''j''th subunit is
. These proportional abundances are weighted by the proportion of data that each subunit contributes to the dataset,
, where
is the total number of individuals in the dataset, and
is the total number of individuals in subunit j. The denominator hence equals mean proportional species abundance within the subunits (mean
) as calculated with the weighted generalized mean with exponent ''q'' - 1.
If the second approach is used, the equation is:
: