hpie {benthos}

Hurlbert's Probability of Interspecific Encounter (PIE)

Description

The probability that two individuals selected at random (without replacement) from a sample will belong to different species is given by (Hurlbert, 1971, p.579, Eq. 3):

\Delta_1 = \sum_{i=1}^S (\frac{N_i}{N})(\frac{N-N_i}{N-1}) = (\frac{N}{N-1})\Delta_2

where \Delta_2 (Hurlbert, 1971, p.579, Eq. 4) is the probability that two individuals selected at random (with replacement) from a sample will belong to different species:

\Delta_2 = 1 - \sum_{i=1}^S \pi_i^2

where N_i is the number of individuals of the ith species in the community, N is the total number of individuals in the community, \pi_i = N_i/N, and S is the number of species in the community. Note that Hurlbert's PIE hpie is the complement of simpson.

Usage

hpie(.data = NULL, taxon, count)

hpie_(.data = NULL, taxon, count)

Arguments

.data

data in a data.frame, tibble, data.table, database etc.

taxon

name of column in .data containing taxa

count

name of column in .data containing counts

Value

A numeric vector with the probability of interspecific encounter (PIE).

Functions

• hpie_(): suitable for calling from a function (see package lazyeval).

References

Hurlbert, S.H., 1971. The Nonconcept of Species Diversity: A Critique and Alternative Parameters. Ecology 52:577-586.

See Also

simpson, hurlbert

Examples

     hpie(
         taxon = c("Euspira pulchella", "Nephtys cirrosa"), 
         count = c(6, 12)
     )