# ens.ht Effective Number of Species with the Horvitz-Thompson Correction

### Description

Calculates diversity profile (DP) using the effective number of species (ENS) based on inverting the Renyi entropy with the Horvitz-Thompson correction. For any monotone diversity index (see, e.g., Rempala and Seweryn 2013) the ENS is defined as the size of a uniform population with the same index value as the current population. The ENS may be considered as a measure of population diversity expressed in the units of species counts. The ENS profile is calculated against the Renyi entropy index, which allows for a direct comparison with the diversity profile (as in `dp`

). The ENS without the Horvitz-Thompson correction is available as function `ens`

. For more details on ENS see Rempala and Seweryn (2013) or Jost (2006).

### Usage

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### Arguments

`x` |
a matrix containing input populations |

`alpha` |
a vector containing alpha values, default = seq(0.1, 2, 0.1) |

`CVG` |
a list containing alpha values multiplied by coverage; default = FALSE |

`CI` |
Confidence Interval default = 0.95, range (0, 1) |

`resample` |
set number of repetitions, default = 100 |

`single_graph` |
default = FALSE, plot of the Diversity Profile for each population; |

`pooled_graph` |
default = FALSE, plot of the Diversity Profile for all populations; |

`csv_output` |
save the result of the analysis as .CSV file, default = FALSE; |

`PlugIn` |
standard plug-in estimator, default = FALSE |

`size` |
resampled fraction of the population, default = 1 (actual size of populations). The value should not be smaller than 10% of population (size = 0.1) |

`saveBootstrap` |
Saves bootstrap result to a file. Use saveBootstrap = TRUE to save bootstrap results to a Bootstrap folder in current directory; saveBootstrap = 'FolderName' - saves bootstrap results to user-named folder |

### Author(s)

Maciej Pietrzak, Michal Seweryn, Grzegorz Rempala

Maintainer: Maciej Pietrzak pietrzak.20@osu.edu

### References

Jost L. (2006) Entropy and diversity. Oikos 113:363-75

Rempala G.A., Seweryn M. Methods for diversity and overlap analysis in T-cell receptor populations. (2013) J Math Biol 67:1339-68

### Examples

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