simpson {abdiv} | R Documentation |

These measures are based on the sum of squared species proportions. The
function `dominance()`

gives this quantity, `simpson()`

gives one
minus this quantity, `invsimpson()`

gives the reciprocal of the
quantity, and `simpson_e`

gives the reciprocal divided by the number
of species.

simpson(x) dominance(x) invsimpson(x) simpson_e(x)

`x` |
A numeric vector of species counts or proportions. |

For a vector of species counts `x`

, the dominance index is defined as

*D = ∑_i p_i^2,*

where *p_i* is the species proportion,
*p_i = x_i / N*, and *N* is the total number of counts. This is
equal to the probability of selecting two individuals from the same species,
with replacement. Relation to other definitions:

Equivalent to

`dominance()`

in`skbio.diversity.alpha`

.Similar to the

`simpson`

calculator in Mothur. They use the unbiased estimate*p_i = x_i (x_i - 1) / (N (N -1))*.

Simpson's index is defined here as *1 - D*, or the probability of
selecting two individuals from different species, with replacement. Relation
to other definitions:

Equivalent to

`diversity()`

in`vegan`

with`index = "simpson"`

.Equivalent to

`simpson()`

in`skbio.diversity.alpha`

.

The inverse Simpson index is *1/D*. Relation to other definitions:

Equivalent to

`diversity()`

in`vegan`

with`index = "invsimpson"`

.Equivalent to

`enspie()`

in`skbio.diversity.alpha`

.Similar to the

`invsimpson`

calculator in Mothur. They use the unbiased estimate*p_i = x_i (x_i - 1) / (N (N -1))*.

Simpson's evenness index is the inverse Simpson index divided by the
number of species observed, *1 / (D S)*. Relation to other definitions:

Equivalent to

`simpson_e()`

in`skbio.diversity.alpha`

.

Please be warned that the naming conventions vary between sources. For
example Wikipedia calls *D* the Simpson index and *1 - D* the
Gini-Simpson index. We have followed the convention from `vegan`

, to
avoid confusion within the `R`

ecosystem.

The value of the dominance (*0 < D ≤q 1*), Simpson index, or
inverse Simpson index. The dominance is undefined if the vector sums to
zero, in which case we return `NaN`

.

x <- c(15, 6, 4, 0, 3, 0) dominance(x) # Simpson is 1 - D simpson(x) 1 - dominance(x) # Inverse Simpson is 1/D invsimpson(x) 1 / dominance(x) # Simpson's evenness is 1 / (D * S) simpson_e(x) 1 / (dominance(x) * richness(x))

[Package *abdiv* version 0.2.0 Index]