fisher.rSAC {preseqR}

Logseries estimator

Description

fisher.rSAC estimates the expected number of species represented at least r times in a random sample, based on the initial sample. The estimator was originally proposed by Fisher et al. (1943) for estimating the SAC. We generalize this estimator for predicting the r-SAC.

Usage

fisher.rSAC(n, r=1)

Arguments

n

A two-column matrix. The first column is the frequency j = 1,2,\dots; and the second column is N_j, the number of species with each species represented exactly j times in the initial sample. The first column must be sorted in an ascending order.

r

A positive integer. Default is 1.

Value

The estimator for the r-SAC. The input of the estimator is a vector of sampling efforts t, i.e., the relative sample sizes comparing with the initial sample. For example, t = 2 means a random sample that is twice the size of the initial sample.

Author(s)

Chao Deng

References

Fisher, R., Corbet, A., & Williams, C. (1943). The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population. Journal of Animal Ecology, 12(1), 42-58. doi:10.2307/1411

Deng, C., Daley, T., Calabrese, P., Ren, J., & Smith, A.D. (2016). Estimating the number of species to attain sufficient representation in a random sample. arXiv preprint arXiv:1607.02804v3.

Examples

## load library
library(preseqR)

## import data
data(WillButterfly)

## construct the estimator for SAC
fisher1 <- fisher.rSAC(WillButterfly, r=1)
## The number of species represented at least once in a sample, 
## when the sample size is 10 or 20 times of the initial sample
fisher1(c(10, 20))

## construct the estimator for r-SAC
fisher2 <- fisher.rSAC(WillButterfly, r=2)
## The number of species represented at least twice in a sample, 
## when the sample size is 50 or 100 times of the initial sample
fisher2(c(50, 100))