Description Usage Arguments Details Author(s) References Examples

View source: R/mobr_boxplots.R

`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).

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`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 |

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().

Dan McGlinn, Thore Engel

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.

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