# hpie: Hurlbert's Probability of Interspecific Encounter (PIE) In benthos: Marine Benthic Ecosystem Analysis

## 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):

Δ1 = ∑_{i=1}^S (N[i]/N)((N-N[i])(N-1)) = (N/(N-1))Δ2

where Δ2 (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:

Δ2 = 1 - ∑_{i=1}^S π[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, π[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

 ```1 2 3``` ```hpie(.data = NULL, taxon, count) hpie_(.data = NULL, taxon, count) ```

## Arguments

 `.data` data in a `data.frame`, `data_frame`, `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.

`simpson`, `hurlbert`

## Examples

 ```1 2 3 4 5``` ``` hpie( taxon = c("Euspira pulchella", "Nephtys cirrosa"), count = c(6, 12) ) ```

### Example output

```[1] 0.4705882
```

benthos documentation built on May 2, 2019, 12:37 p.m.