# calc_PIE: Calculate probability of interspecific encounter (PIE) In MoBiodiv/mobr: Measurement of Biodiversity in R

## Description

`calc_PIE` returns the probability of interspecific encounter (PIE) which is also known as Simpson's evenness index and Gini-Simpson index. For `ENS=TRUE`, PIE will be converted to an asymptotic effective number of species (S_PIE).

## Usage

 `1` ```calc_PIE(x, ENS = FALSE) ```

## Arguments

 `x` can either be a: 1) mob_in object, 2) community matrix-like object in which rows represent plots and columns represent species, or 3) a vector which contains the abundance of each species. `ENS` boolean that determines if the effective number of species should be returned or the raw PIE value. Defaults to FALSE

## Details

The formula of Hurlbert (1971) is used to calculate PIE:

PIE = N /(N - 1) * (1 - p_i^2)

where N is the total number of individuals and p_i is the relative abundance of species i. This formulation uses sampling without replacement and it is sometimes referred to as the bias corrected formulation of PIE.

For `ENS = TRUE`, S_PIE will be returned which represents the species richness of a hypothetical community with equally-abundant species and infinitely many individuals corresponding to the observed value of PIE. It is computed as S_PIE = 1 /(1 - PIE), which is equal to the asymptotic estimator for Hill numbers of diversity order 2 provided by Chao et al (2014). Note that S_PIE is undefined for communities with exactly one individual per species.

The code in this function borrows heavily from the function vegan::diversity() but computes a different quantity. The function vegan::diversity() computes PIE when sampling with replacement is assumed. The difference between the two formulations will decrease as N becomes large. Jari Oksanen and Bob O'Hara are the original authors of the function vegan::diversity().

## Author(s)

Dan McGlinn, Thore Engel

## References

Hurlbert, S. H. (1971) The nonconcept of species diversity: a critique and alternative parameters. Ecology 52, 577<e2><80><93>586.

Chao, A., Gotelli, N. J., Hsieh, T. C., Sander, E. L., Ma, K. H., Colwell, R. K., & Ellison, A. M. (2014). Rarefaction and extrapolation with Hill numbers: A framework for sampling and estimation in species diversity studies. Ecological Monographs 84(1), 45<e2><80><93>67.

## Examples

 ```1 2 3``` ```data(inv_comm) calc_PIE(inv_comm) calc_PIE(inv_comm, ENS=TRUE) ```

MoBiodiv/mobr documentation built on May 7, 2019, 4:58 p.m.