# fisher.rSAC: Logseries estimator In preseqR: Predicting Species Accumulation Curves

## 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

 `1` ```fisher.rSAC(n, r=1) ```

## Arguments

 `n` A two-column matrix. The first column is the frequency j = 1,2,…; 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.

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## 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)) ```

### Example output

```There were 20 warnings (use warnings() to see them)
[1] 332.5787 360.4707
There were 20 warnings (use warnings() to see them)
[1] 357.1006 384.9958
```

preseqR documentation built on May 2, 2019, 6:39 a.m.