# fisher

##### Various functionality to implement Fisher's logseries

Various functions connected to Fisher's logseries including creation of synthetic datasets and estimation of Fisher's alpha

- Keywords
- math

##### Usage

```
fishers.alpha(N, S, give=FALSE)
fisher.ecosystem(N, S, nmax, alpha=NULL, c=0)
```

##### Arguments

- N
Size of the ecosystem. In the case of

`fisher.ecosystem()`

, the expected size of the ecosystem- S
Number of species in ecosystem

- alpha
In function

`fisher.ecosystem()`

, Fisher's \(\alpha\). If not supplied, it will be calculated from`N`

and`S`

.- give
In function

`fishers.alpha()`

, Boolean variable with default`FALSE`

meaning to return alpha, and`TRUE`

meaning to return a list containing`x`

and`alpha`

.- nmax
In function

`fisher.ecosystem()`

, the maximum number of species abundance classes to consider- c
In function

`fisher.ecosystem()`

, the rare species advantage term

##### Details

Function `fishers.alpha()`

solves for \(\alpha\) given
\(N\) and \(S\), as per Fisher's table 9, p55.

Given \(N\) and \(S\) (or \(\alpha\)), function
`fisher.ecosystem()`

generates a Fisherian ecosystem
with expected size \(N\) and expected species count \(S\).

##### References

R. A. Fisher and A. S. Corbet and C. B. Williams 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*, volume 12, pp 42--58

##### Examples

```
# NOT RUN {
fishers.alpha(N=100000,S=100)
#compare the Table value:
100000/10^3.95991
# }
```

*Documentation reproduced from package untb, version 1.7-4, License: GPL*