hpie {benthos} R Documentation

## 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):

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

```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.

### See Also

`simpson`, `hurlbert`

### Examples

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

```

[Package benthos version 1.3-6 Index]